Physical lecture 2

Question 1

State the fundamental equation for the speed of an EM wave

Answer 1

c = fλ
c is the speed of the wave
f is the frequency
λ is the wavelength

Question 2

State the multiplier for the prefix ‘nano’

Answer 2

10^-9

Question 3

Define one Å

Answer 3

Å represents ‘angstrom’. One angstrom = 1x10^-10m

Question 4

Define wavenumber (v~) and relate it to photon energy

Answer 4

1/λ, measured in (length)-1. We can get E = hcv~, so photon energy is proportional to wavenumber. It is an energy equivalent unit

Question 5

State how to convert from m^-1 to cm^-1

Answer 5

Divide by 100

Question 6

Describe the emission spectra of the hydrogen atom

Answer 6

There are many lines which are clearly in groups (ie series), with each series of lines converging with decreasing wavelengths/ an increasing photon energy. All lines in a series have the same value of n1. The names correspond to the scientists who observed them.

Question 7

Give Bohr’s equation for wavenumber and explain the terms

Answer 7

v~ = -RH(1/n2^2 - 1/n1^2), usually measured in cm-1
RH is the Rydberg constant for the hydrogen atom.
n2 is the quantum number of the upper level of the transition, and n1 the number of the lower level
n2 > n1

Question 8

State the names of the first four series and their values of n1

Answer 8

Lyman (n1 = 1), Balmer (n1 = 2) , Paschen (n1 = 3) and Brackett (n1 = 4)

Question 9

Describe Bohr’s explanation of his equation for wavenumber

Answer 9

He said the electron orbiting the nucleus must be confined to specific orbits of fixed energies, with each orbit having a different value of n

Question 10

Give the energy level expression for the hydrogen atom in joules and wavenumbers

Answer 10

-hcR/n^2 in joules
-R/n^2 in wavenumbers
n is the principle quantum number

Question 11

Define the zero of energy

Answer 11

Also known as the ionisation limit, where n = ∞, this is defined as a separated proton and electron. From this we can see why orbital energies are negative.

Question 12

Describe how to determine the value of R in the energy level expression for an atom

Answer 12

Start by looking at values of wavenumber of lines in one series; all values of n1 will be the same so 1/n1^2 can be labelled as a constant c. Now the Bohr equation resembles that of a straight line, and -R can be found by calculating the gradient of this line

Question 13

Describe the Rydberg constant

Answer 13

Rx is calculated using values of wavenumber for a particular atom. It differs slightly for different atoms.

Question 14

Describe Bohr’s three postulates that quantitatively explain the energy level equation for the hydrogen atom

Answer 14

• Electrons move in circular orbits around the nucleus
• Only certain orbits are allowed, ie those with integer values of n. While in these orbits, electrons do not emit energy.
• A single photon is emitted or absorbed when an electron moves into a different orbital

Question 15

Give the equation that gives the force required to keep a particle in its circular orbit and explain the terms

Answer 15

F = - mv^2/r
F = force
m = mass of the particle
v = velocity of the particle
r = radius of the orbit
Note the negative sign: force is in the opposite direction to the radius, ie it points towards the centre of the orbit

Question 16

Give the equation for linear momentum

Answer 16

p = mv 
p = momentum 
m = mass 
v = velocity

Question 17

Describe angular momentum

Answer 17

It is a vector quantity and its direction is perpendicular to the plane of rotation. It is important as electrons and photons have angular momentum which is usually conserved in chemical processes.

Question 18

Give the equation for angular momentum and explain the terms

Answer 18

L = Iω
I is the moment of inertia; the angular equivalent of mass
ω (omega) is the angular velocity in rads-1

Question 19

Describe I, the moment of inertia

Answer 19

I is the sum over all the masses that make up the body multiplied by the square of their distance from the axis of rotation. Ie heavy objects with a lot of mass far from the axis of rotation have a large moment of inertia