nuclei

Question 1

Activity

Answer 1

Also called decay rate
A_c = -dN/dt

dN- decrease in no of nuclei

Question 2

Units of activity

Answer 2

dps (decay per second)
1 Bq (Becquerel) = 1 dps
1 Ci (Curie) = 3.7 * 10¹⁰ dps
= 3.7 * 10¹⁰ Bq
1 Ru (Rutherford) = 10⁶ dps

Question 3

Radioactive decay law

Answer 3

Activity ∝ Number of active nuclei
-dN/dt = λN
where λ is the decay constant (tells how fast decay occurs)

N = N_oe^-λt
N_o is the no. of nuclei at t=0

A_c = A_coe^-λt

Question 4

half life

Answer 4

T = ln 2/λ
ln 2 = 0.693

Question 5

Mean life time

Answer 5

Tau = 1/λ

Question 6

Simultaneous decay

Answer 6

N = N_oe^{-(λ₁ + λ₂) t}

A =λ₁N + λ₂N

-dN/dt = N(λ₁ + λ₂)

Question 7

no. of half lives

Answer 7

y= 1/2ⁿ
y = amt of radioactive substance left
n = no of half lives

Question 8

Size of nucleus

Answer 8

R = R_oA^1/3
R_o= fermi const= 10^-15

Question 9

mass defect

Answer 9

Δm = [Z(m_p) + (A-Z)m_n - M]

where Z= at. no.
m_p = mass of proton
A = Mass no.
m_n = mass of neutron
M = mass of nucleus

Question 10

linear momentum eqn for alpha decay

Answer 10

M_YV_Y = M_αV_α

Question 11

Kinetic energy of system

Answer 11

Q= 1/2 M_YV_Y² + 1/2 M_αV_α²

Question 12

KE of alpha

Answer 12

K_α = QM_Y / (M_α + M_Y)

K_α= Q(A-4)/A
A= mass no

Question 13

K capture

Answer 13

proton + electron –> neutrino + neutron

electron is captured from K shell