Nuclei Easy Questions and Answers | Page - 14

Nuclei

Half-lives of two radioactive substances A and B are respectively 20 minutes and 40 minutes. Initially, the samples of A and B have equal number of nuclei. After 80 minutes the ratio of remaining numbers of A and B nuclei is

1. 1 : 16
1. 4 : 1
1. 1 : 4
1. 1 : 1

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80 = 20 × n_A ⇒ n_A = 4
80 = 40 × n_B ⇒ n_B = 2
= 1 ²
N_A 2
N_B 1 ²
2

= 1 × 1 = 1
2 2 4

Correct Option: C

80 = 20 × n_A ⇒ n_A = 4
80 = 40 × n_B ⇒ n_B = 2
= 1 ²
N_A 2
N_B 1 ²
2

= 1 × 1 = 1
2 2 4

The activity of a radioactive sample is measured as 9750 counts per minute at t = 0 and as 975 counts per minute at t = 5 minutes. The decay constant is approximately

1. 0.922 per minute
1. 0.691 per minute
1. 0.461 per minute
1. 0.230 per minute

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dN = KN
dt

9750 = KN₀ .............(1)
975 = KN .............(2)
Dividing (1) by (2)
N = 1
N₀ 10

K = 2.303 log N₀ = 2.303 log10
t N 5

= 0.4606 = 0.461 per minute

Correct Option: C

dN = KN
dt

9750 = KN₀ .............(1)
975 = KN .............(2)
Dividing (1) by (2)
N = 1
N₀ 10

K = 2.303 log N₀ = 2.303 log10
t N 5

= 0.4606 = 0.461 per minute

A free neutron decays into a proton, an electron and

1. a beta particle
1. an alpha particle
1. an anti-neutrino
1. a neutrino

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₀n¹ → ₁p¹ + _{- 1}e⁰ + X
X must have zero charge and almost zero mass as electron is emitted. Hence X must be anti-neutrino.

Correct Option: C

₀n¹ → ₁p¹ + _{- 1}e⁰ + X
X must have zero charge and almost zero mass as electron is emitted. Hence X must be anti-neutrino.

The most penetrating radiation of the following is

1. gamma-rays
1. alpha particles
1. beta-rays
1. X-rays

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The penetrating power of radiation is directly proportional to the energy of its photon.
Energy of a photon
= hc ∝ 1
λ λ

∴ Penetrating power ∝ 1
λ

λ is minimum for γ-rays, so penetrating power is maximum of γ-rays.

Correct Option: A

The penetrating power of radiation is directly proportional to the energy of its photon.
Energy of a photon
= hc ∝ 1
λ λ

∴ Penetrating power ∝ 1
λ

λ is minimum for γ-rays, so penetrating power is maximum of γ-rays.

What is the respective number of α and β-particles emitted in the following radioactive decay ²⁰⁰X₉₀ → ¹⁶⁸X₈₀?

1. 6 and 8
1. 6 and 6
1. 8 and 8
1. 8 and 6

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²⁰⁰X₉₀ → ¹⁶⁸Y₈₀.
We know that
²⁰⁰X₉₀ → n₂He⁴ + m_{- 1}β⁰ + ¹⁶⁸Y₈₀.
Therefore, in this process,
200 = 4n + 168
or n = 200 - 168 = 8.
4

Also, 90 = 2n – m + 80
or, m = 2n + 80 – 90 = (2 × 8 + 80 – 90) = 6.
Thus, respective number of α and β-particles will be 8 and 6.

Correct Option: D

²⁰⁰X₉₀ → ¹⁶⁸Y₈₀.
We know that
²⁰⁰X₉₀ → n₂He⁴ + m_{- 1}β⁰ + ¹⁶⁸Y₈₀.
Therefore, in this process,
200 = 4n + 168
or n = 200 - 168 = 8.
4

Also, 90 = 2n – m + 80
or, m = 2n + 80 – 90 = (2 × 8 + 80 – 90) = 6.
Thus, respective number of α and β-particles will be 8 and 6.