Q: The half-life of radium is about 1600 yr. Of 100 g of radium existing now, 25 g will remain unchanged after

3200 yr. \frac{25}{100} = \frac{1}{4} = \left(\frac{1}{2}\right)^2 — 2 half-lives t = 2 \times 1600 = 3200 yr

Q: Half-life of a radioactive substance is 12.5 h and its mass is 256 g. After what time, the amount of remaining substance is 1 g?

100 h. \frac{1}{256} = \left(\frac{1}{2}\right)^8 — 8 half-lives t = 8 \times 12.5 = 100 h

Q: Half-life period of a radioactive substance is 6 h. After 24 h activity is 0.01 µC, what was the initial activity?

0.16 µC. 24 h = 4 half-lives R_0 = 0.01 \times 2^4 = 0.16 µC

Q: The half-life of a radioactive material is 3 h. If the initial amount is 300 g, then after 18 h, it will remain

4.68 g. 18 h = 6 half-lives N = 300 \times \frac{1}{64} = 4.68 g

Question 1

What happens to the mass number and atomic number of an element when it emits \gamma-radiation?

Accepted Answer

Mass number and atomic number remain unchanged. \gamma-radiation is just a high-energy photon — its emission changes neither the atomic number nor the mass number.

Question 2

\alpha-particle consists of

Accepted Answer

2 protons and 2 neutrons only. An \alpha-particle is a doubly ionised helium nucleus (He²⁺) — 2 protons and 2 neutrons, with no electrons.

Question 3

The half-life of radium is about 1600 yr. Of 100 g of radium existing now, 25 g will remain unchanged after

Accepted Answer

3200 yr. \frac{25}{100} = \frac{1}{4} = \left(\frac{1}{2}ight)^2 — 2 half-lives

t = 2 	imes 1600 = 3200 yr

Question 4

A nuclear reaction given by ^{A}_{Z}X ightarrow\ ^{A}_{Z+1}Y +\ ^{0}_{-1}e + \bar{
u} represents

Accepted Answer

\beta-decay. Emission of an electron (^{0}_{-1}e) and an antineutrino with Z increasing by 1 is \beta^- decay.

Question 5

The mass number of a nucleus is

Accepted Answer

sometimes equal to its atomic number. Mass number = protons + neutrons. For ordinary hydrogen (no neutrons) the mass number equals the atomic number; otherwise it is greater. So it is sometimes equal.

Question 6

Half-life of a radioactive substance is 12.5 h and its mass is 256 g. After what time, the amount of remaining substance is 1 g?

Accepted Answer

100 h. \frac{1}{256} = \left(\frac{1}{2}ight)^8 — 8 half-lives

t = 8 	imes 12.5 = 100 h

Question 7

Half-life period of a radioactive substance is 6 h. After 24 h activity is 0.01 µC, what was the initial activity?

Accepted Answer

0.16 µC. 24 h = 4 half-lives

R_0 = 0.01 	imes 2^4 = 0.16 µC

Question 8

Which of the following is positively charged?

Accepted Answer

\alpha-particle. X-rays and \gamma-rays are electromagnetic waves (no charge); \beta-particles are negatively charged electrons. The \alpha-particle (helium nucleus) is positively charged.

Question 9

The half-life of a radioactive material is 3 h. If the initial amount is 300 g, then after 18 h, it will remain

Accepted Answer

4.68 g. 18 h = 6 half-lives

N = 300 	imes \frac{1}{64} = 4.68 g

Question 10

The relationship between disintegration constant (\lambda) and half-life (T) will be

Accepted Answer

\lambda = \frac{\log_e 2}{T}. From 0.5N_0 = N_0e^{-\lambda T}: \lambda T = \log_e 2

\lambda = \frac{\log_e 2}{T}

Question 11

Alpha particles are

Accepted Answer

doubly ionised helium atoms. An \alpha-particle is a helium nucleus — a helium atom stripped of both its electrons, i.e. a doubly ionised helium atom.

Question 12

A free neutron decays into a proton, an electron and

Accepted Answer

an antineutrino. ^{1}_{0}n ightarrow\ ^{1}_{1}H + \beta^- + \bar{
u}

A free neutron decays into a proton, an electron and an antineutrino.

Question 13

The most penetrating radiation out of the following is

Accepted Answer

\gamma-rays. Penetrating power increases with photon energy (\propto \frac{1}{\lambda}). \gamma-rays have the shortest wavelength, hence the maximum penetrating power.

Question 14

The mass number of He is 4 and that for sulphur is 32. The radius of sulphur nuclei is larger than that of helium by

Accepted Answer

2. R \propto A^{1/3}

\frac{R_S}{R_{He}} = \left(\frac{32}{4}\right)^{1/3} = 2

Question 15

If the nuclear force between two protons, two neutrons and between proton and neutron is denoted by F_{pp}, F_{nn} and F_{pn} respectively, then

Accepted Answer

F_{pp} = F_{nn} = F_{pn}. Nuclear forces are charge independent — they act between n–n, p–p and n–p pairs with the same strength.

Question 16

In the nucleus of _{11}Na²³, the number of protons, neutrons and electrons are

Accepted Answer

11, 12, 0. Protons = Z = 11; neutrons = A - Z = 23 - 11 = 12; there are no electrons inside the nucleus.

Question 17

The half-life of radium is 1600 yr. The fraction of a sample of radium that would remain after 6400 yr is

Accepted Answer

\frac{1}{16}. n = \frac{6400}{1600} = 4 half-lives

\frac{N}{N_0} = \left(\frac{1}{2}\right)^4 = \frac{1}{16}

Question 18

The constituents of atomic nuclei are believed to be

Accepted Answer

neutrons and protons. A nucleus of mass number A and atomic number Z contains Z protons and (A − Z) neutrons — nucleons only.

Question 19

Which of the following statements is true for nuclear forces?

Accepted Answer

They are short range forces. Nuclear forces are short-range (a few fermi), charge-independent, non-central and are the strongest forces in nature — about 100 times the electrostatic force.

Question 20

A radioactive element has half-life period 800 yr. After 6400 yr, what amount will remain?

Accepted Answer

\frac{1}{256}. n = \frac{6400}{800} = 8 half-lives

\frac{N}{N_0} = \left(\frac{1}{2}\right)^8 = \frac{1}{256}

Nucleus and Radioactivity — JEE Main Physics MCQs with Solutions

Questions with solutions