The Hydrogen Spectrum

Question 1

Define wavelength

Answer 1

Wavelength is defined as the distance between two successive peaks.

Question 2

Define frequency

Answer 2

Frequency is defined as the number of vibrations per second.

Question 3

Briefly explain electromagnetic radiation

Answer 3

Electromagnetic radiation is energy that can travel through a vacuum. The most familiar form is light but other types include infrared, radio waves and X-rays.

Electromagnetic radiation can be thought of as a continuous wave, and therefore can be characterised by wavelength (upside down y symbol called lambda) and frequency (f).

Question 4

On the visible spectrum, what is the high energy colour and the low energy colour?

Answer 4

High energy colour - blue
Low energy colour - red

Question 5

High energy = ___ frequency & ___ wavelength

Low energy = ___ frequency & ___ wavelength

Answer 5

High energy =
high frequency & short wavelength
(Number of waves per second is high)

Low energy =
low frequency & long wavelength
(Number of waves per second is low)

Question 6

Which equation links wavelength and frequency?

Answer 6

C=(lambda)F

*where c = velocity of
electromagnetic radiation in a vacuum (3x10°ms-1)
*Frequency is measured in Hz (s-1)
*Wavelength is measured in metres

Question 7

How do you convert Hz to MHz?

Answer 7

1 Hz -> 1 x 10^-6 MHz

Question 8

How would you covert nm to m?

Answer 8

1nm -> 1 x 10^-9 m

To convert from nm to m add ‘1x10^-9’

Question 9

UV, visible and infrared regions.
What has the shortest wavelength? The longest?

Answer 9

Shortest wavelength = UV
(Around (400nm)

Longest wavelength = IR

Question 10

What is the continuous visible spectrum?

Answer 10

If white light is passed through a prism, the light is spilt into a rainbow of colours.

Question 11

Wave/particle duality

Answer 11

There are two different ways of representing light; either as a wave or as a particle.
When thought of as a particle we consider light as consisting of a series of discrete packets of energy (or quanta of energy) called photons that have a specific frequency rather than as a continuous wave;

Question 12

What’s a photon?

Answer 12

Photons are packets of energy called quanta (or quantised amounts of energy)

Specific energy/frequencies

Question 13

How are black lines produced in an absorption spectrum?

Answer 13

Atoms can absorb photons of light
& The energy of the photon can be transferred to the electrons in an atom.
This causes electrons to be promoted and jump from a lower energy level to a higher energy level. (The higher the energy/frequency of the photon. the bigger the electron jumps)

A spectrum can be produced to show this absorption and it appears as sharp black lines appear against a bright background.

Question 14

Note to read, if you want

Answer 14

Note; The black lines represent the energy/wavelength/frequency of the coloured photons that used to be present but have now been absorbed into the atom. (Think of this process a little like when food absorbs microwaves and as a result the food becomes hotter - in a similar manner, photons become absorbed into an atom, and as a result the electrons jump up). Therefore the frequency of the photon will be the same as the frequency of the black line.

Question 15

Why are the black lines sharp in an absorption spectrum?

Answer 15

The lines are sharp since photons are absorbed and these have very specific energies and frequencies (quantised amount of energy) and therefore the black lines (which show that photons have been absorbed)
also appear sharp.

The energy absorbed must be a correct precise amount (a photon) to allow the electron to jump to the next shell (or a higher shell) in an atom. We know that electrons are constrained to energy levels and can only move between distinct regions in an atom. This means that electrons have to absorb a specific frequency/quantised energy e.I. A photon. This means that the electron has a quantised energy.
Therefore the energy of the photon must correspond exactly to the difference in energy between the two shells that the electron hops between This also helps to explain why the black lines are sharp.

Question 16

Another note to ready if you want to

Answer 16

We use absorption spectroscopy to observe elements in the atmosphere of our planet or other stars; light from the sun passes through the cool gases in the atmosphere and when we use a spectrometer we see black lines. This means that elements in the atmosphere are absorbing different frequencies of visible light, causing their electrons to jump up to higher energy levels. Other frequencies may also be absorbed such as I and UV however our eyes cannot detect this on the spectrometer

Question 17

Tip: ‘Light’ can mean UV, visible or
IR so you need to check which type of light a question is referring to!

Question 18

Some atoms absorb a red photon, why? When?

Answer 18

This can only happen if the photon has the correct energy to make an electron jump from shell 2 to shell 3

Question 19

Some atoms may absorb a blue photon, why? When?

Answer 19

This can only happen if the photon has the correct energy to make an electron jump from shell 2 to shell 5

Question 20

What are the features of the hydrogen absorption spectrum?

Answer 20

Bright background with black lines

Absorption produces dark sharp lines against a bright background by passing light through a cool gas. A cool gas means that the electrons are jumping from the ground state.

Question 21

An absorption spectrum was produced form elements in the atmosphere absorbing the light from the sun. How did scientists identify which element is which?

Answer 21

One way would be to use emission spectroscopy

Question 22

Features of the emission spectrum

Answer 22

Dark background with bright lines when a sample is heated

Question 23

Equations

E =
h =
F =
c =
Upside down y (lambda) =

Answer 23

E = energy (joules)
h = planck’s constant (6.626x10^-34 J.s)
F = frequency do radiation (Hz)
c = 3x10^8 ms^-1
Upside down y = metres

Question 24

What equation would you use to calculate the energy of a photon (and the energy of the line)?

You are given energy and frequency

Answer 24

E=hF

Question 25

What equation would you use to calculate the energy of a photon (and the energy of the line)?

You are given frequency and wavelength

Answer 25

c = (lambda)F

Question 26

What equation would you use to calculate the energy of a photon (and the energy of the line)?

Answer 26

E = hc/(lambda)

Question 27

If an electron in an atom jumps between shells 1 and 2, then a photon must be equal to the difference in energy between these shells to cause an electron to jump, so how do we write the equation?

Answer 27

E1 - E2 =hf

Question 28

How to you convert J to KJ?

Answer 28

Divide by 1,000

Question 29

How do you covert micrometers to metres?

Answer 29

Divide by 1,000,000

Question 30

How do you convert nm to m?

Answer 30

Divide by 1,000,000,000

Question 31

How to covert MHz to Hz?

Answer 31

Divide by 1,000,000

Question 32

Steps to working out the energy of a molecule/line from its wavelength or frequency;

Answer 32

Step 1; If wavelength has been given in the question, ensure that it is in metres. To convert nm to m add x10 ^-9 to the wavelength number. (200m = 200×10^-9m)
Step 2a; If energy needs to be calculated from wavelength use the equation; E=hc/(lambda)
Step 2b; If energy needs to be calculated from frequency, use the equation; E = ht
Step 3: Your answer will be in Joules, so if the energy needs to be in KJ then divide by 1000.
Step 4; If the answer is needed in KJmol^-1, then multiply your answer, in three steps, by Avogadro’s number (6x10^23)

Question 33

Explain the origin of the lines
or
How are lines produced in the hydrogen emission spectrum?

Answer 33

@ Hydrogen is heated to produce a hot gas (or an electrical discharge is
passed through it)
@ Atoms absorb energy and this causes electrons to be promoted and jump
from a lower energy level to a higher energy level.
@Eventually the electrons fall back down from a higher energy level to a lower energy level and photons of light are emitted.

Question 34

Why are sharp lines produced in the emission spectrum of hydrogen?

Answer 34

@ Electrons are constrained to energy levels and the jump that the electron makes is very specific and quantised. (Shells are quantised). This means the energy of the electron is quantised.
@ Therefore the photons emitted have very sharp and discrete packets of energies/frequencies (Since the energy emitted is equal to the difference between two energy levels).
@ This creates sharp bright lines
© A spectrum can be produced to show this emission and it appears as sharp bright lines against a dark background.

Question 35

What does the hydrogen emission spectrum look like?

Answer 35

Lines get closer and closer together and eventually reach the “series limit”

The convergence limit
n = infinite

Question 36

When an electron jumps down to shell 2, what series is it in?

Answer 36

Balmer series
(Partially visible)

Lower frequency

Question 37

When an electron jumps down to shell 1, what series is it in?

Answer 37

Lyman series
(Ultra-violet)

Higher frequency

Question 38

Am electron jumps up to shell 3. This electron would tend to lose energy by falling to a lower level. It could do this in two different ways:

Answer 38

*It could fall all the way back down to the first level again (shell 1) emitting
UV light.
*Or, it could fall back to the second level (shell 2) emitting visible light in the red region (and then in a second jump, down to shell 1 emitting UV light).

Question 39

An electron jumps up to shell 5. This electron would tend to lose energy by falling to a lower level. It could do this in a number of different ways, for example it could;

Answer 39

*Fall all the way back down to the first level (shell 1) emitting UV light.
*Or, it could fall back to shell 2 first emitting visible light in the blue region (and then in a second jump, fall down to the first level emitting UV light)

Question 40

Why is visible light produced when electrons jump down to shell 2 and UV produced when electrons jump down to shell 1?

Answer 40

The type of energy that is emitted depends on the size of the jump that an electron makes, the bigger the jump the higher the energy/frequency.
The spacing of the energy levels in hydrogen is such that shell 1 and shell 2 are much further apart than shell 2 and 3. Shell 3 and 4 are closer and 5,6 even closer again and so on. The further away we move from the nucleus of hydrogen the closer the shells become.
This means that jumps to shell 1 are always the biggest jumps and emit the highest frequency’s such as UV. Jumps to shell 2 are smaller and so visible is emitted.

Question 41

Why do we have a convergence limit?

Answer 41

As we move away from the nucleus of the atom, the distance between the shells become reduced and the shells become closer together until the energy levels converge. This happens at n=o and is called the convergence limit. This is why the lines converge in each series of the emission spectrum

Question 42

How are sharp lines produced in the hydrogen emission spectrum?

Answer 42

@ Hydrogen is heated to produce a hot gas (or an electrical discharge is
passed through it)
© Atoms absorb energy and this causes electrons to be promoted and jump
from a lower energy level to a higher energy level.
Eventually the electrons fall back down from a higher energy level to a lower energy level and photons of light are emitted. (equal to the energy difference between the two shells involved).
@ Photons have very sharp and discrete packets of energies/frequencies.
@ This creates sharp visible lines

Question 43

How are sharp bright lines produced in the visible emission spectrum of hydrogen?

Answer 43

© Atoms are excited using an electrical discharge and absorb energy.
This causes electrons to be promoted and jump from a lower energy level to a higher energy level.
@ Eventually the electrons fall back down from a higher energy level to
SHELL 2 and photons of visible light are emitted (equal to the energy difference between the two shells involved).
@ Photons have very sharp and discrete packets of energies/frequencies
© This creates sharp visible lines

Question 44

How are sharp red lines produced i the visible emission spectrum of hydrogen?

Answer 44

© Atoms are excited using an electrical discharge and absorb energy.
This causes electrons to be promoted and jump from a lower energy level up to SHELL 3.
@Eventually the electrons fall back down from SHELL 3 to SHELL 2 and photons of red visible light are emitted (equal to the energy difference between shells 3 and 2).
Red protons because it is a low frequency because it is a smaller jump
@ Photons have very sharp and discrete packets of energies/frequencies
& This creates a sharp red line.

Question 45

Why do the likens in each series (balmer, lyman) converge

Answer 45

The gap between the energy levels in the atom becomes smaller as we move further from the nucleus of an atom. This means that the energy difference for each jump becomes more similar in value as we observe jumps further and further away from the nucleus. Thus the lines of each series converge with increasing energy.

Question 46

How can we find the ionisation energy?

Answer 46

From its emission spectrum

Question 47

What does ionisation energy correspond to?

Answer 47

The removal of an electron from an atom

Question 48

For an electron to be removed it has to jump from ___ to ___ where the electron is then ___ and ___ is formed

Answer 48

The ground state (1s orbital)
To
n = infinity (the convergence limit)

Where the electron is then ‘free’ from the atom and an ion is formed

Question 49

Which series contains an electron transition between n=1 and n=infinity?

Answer 49

The Lyman series

Question 50

What are we measuring to tell us the ionisation energy?

Answer 50

The energy and the frequency of the largest jump in the Lyman series

Question 51

How do we find the ionisation energy of hydrogen?

Answer 51

To find the ionisation energy of hydrogen all we need to do is measure the frequency of the jump between n=1 and n=∞ (convergent frequency) by looking at the line produced in the lyman series of the
emission spectrum of hydrogen and use the equation E = hf