Nuclei

Question 1

Isotope

Answer 1

Same atomic no. (Z), but different mass no. (A)

Eg: ₁H¹ (protium), ₁H² (deuterium), and ₁H³ (tritium) are isotopes of hydrogen

Question 2

Isobar

Answer 2

Same mass no. (A), but different atomic no. (Z)

Eg: ₆C¹⁴, ₇N¹⁴

Question 3

Isotone

Answer 3

Same number of neutrons

Eg: ₁H³, ₂He⁴ (Nₙ=2)

Question 4

Isomer

Answer 4

Same atomic no. and mass no., but different energy levels

Eg: z*Xᴬ, zXᴬ

Question 5

Average Atomic Mass

Answer 5

Aₐᵥ = m₁x₁% + m₂x₂% + m₃x₃% + …

Question 6

Radius of Nuclei

Answer 6

R = Rₒ∛A, Rₒ = 1.2 x 10⁻¹⁵

Question 7

Density of Nucleus

Answer 7

Is constant, regardless the mass no.

ρ = 2.12 x 10¹⁷ kg m⁻³

Question 8

Mass Defect

Answer 8

The difference between the sum of masses of protons and neutrons, and the actual mass of the nucleus
Δm = Zmₚ + (A-Z)mₙ - Mⁿᵘᶜˡᵉᵘˢ

Question 9

Mass-Energy Conservation in Nuclear Reactions

Answer 9

A + B ⟶ C + D + Q [Q→Energy released]
Δm = (Mᴀ+Mʙ) - (Mᴄ+Mᴅ)
Q = Δmc² J [Δm in kg]
= 931.5Δm MeV [Δm in amu]

Question 10

Atomic Mass Unit

Answer 10

1 amu = 1 u = 1/12 (m ₆C¹²) ≈ (1.67 x 10⁻²⁷) kg

E ₁ₐₘᵤ = 931.5 MeV

Question 11

Binding Energy

Answer 11

Energy lost during formation of a nucleus
OR
Energy supplied to separate nucleons of a nucleus to infinite distances apart
Eʙ = Δmc² J [Δm in kg]
= 931.5Δm MeV [Δm in amu]

• It is the reason for mass defect.

Question 12

Binding Energy per Nucleus

Answer 12

Eʙɴ = Eʙ/A

Eʙɴ ∝ Stability of nucleus

Question 13

Light and Heavy Nuclei

Answer 13

Light Nuclei → A < 30
Heavy Nuclei → A > 170
- Both heavy and light nuclei have low Eʙɴ value, i.e.,
they are unstable

Question 14

Middle-Mass Nuclei

Answer 14

30 > A > 170

- Highly stable nuclei

Question 15

Most Stable Nuclei

Answer 15

Fe⁵⁶, Eʙɴ = 8.75 MeV

Question 16

Radioctivity

Answer 16

The phenomena by which unstable nuclei spontaneously emit particles and/or radiations to attain stability

Question 17

Law of Radioactive Decay

Answer 17

The rate of disintegration (dN/dt) at a given time is directly proportional to the number of atoms (i.e., nuclei) present at that time (Nₜ)
(dN/dt) ∝ Nₜ
(dN/dt) = -λNₜ [λ → decay/disintegration constant]

Nₜ = N₀e^(-λt)

Question 18

Half-Life

Answer 18

Time taken to reduce the activity or concentration of a radioactive sample to half its initial value
t = 0.693/λ

Question 19

Mean-Life

Answer 19

Time taken to reduce the activity or concentration of a radioactive sample to 1/e its initial value
𝜏 = λ⁻¹

• λ can be defined as the ti

Question 20

Activity of a Sample

Answer 20

The rate of decay of radioactive nuclei in a sample
Aₜ = λNₜ = A₀e^(-λt) [A₀ = λN₀]

• Units:
  (i) 1 Bq = 1 decay s⁻¹ [Bq → Baquerel]
  (ii) 1 Cu = 3.7 x 10¹⁰ decay s⁻¹ [Cu → Curie]

Question 21

Nuclear Force

Answer 21

Force between the nucleons which keep them together, overcoming even the electrostatic forces of repulsion between the protons

Question 22

Properties of Nuclear Force

Answer 22

(i) Strongest known force
(ii) Short range
(iii) Charge independent
(iv) Shows saturation property
(v) Generally attractive, but can repulsive for very short distances

Question 23

Conclusions from PE vs. Distance Graph for Two Nucleons

Answer 23

(i) Since PE values are in MeV order, nuclear force is very strong
(ii) Since PE approaches zero in a short fermi distance, nuclear force is short range
(iii) Nuclear force can be repulsive (for very short distances) or attractive

Question 24

α - Decay

Answer 24

Process by which unstable nuclei emit α-particle in the process of attaining stability
Eg: ₉₂U²³⁸ ⟶ ₉₀Th²³⁴ + ₂He⁴ + Q

• The daughter element formed has A less by 4 and Z less by 2.
• Q value of α - decay is a characteristic of parent nucleus (same nuclei have same value of Q)

Question 25

α - Particle

Answer 25

α = ₂He⁴ = He nucleus
m = 4mₚ
q = 2qₚ = 2(+e)