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Physics MCQs for NEET — Practice Questions with Answers

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The average life T and the decay constant $λ$ of a radioactive nucleus are related as

$Tλ = 1$

$T = \frac{0.693}{λ}$

$\frac{T}{λ} = 1$

$T = \frac{c}{λ}$

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Explanation

(a) $Average life T = \frac{Sum of all lives of all the atom}{Total number of atoms} = \frac{1}{λ}$

$\Rightarrow Tλ = 1$

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If T is the half life of a radioactive material, then the fraction that would remain after a time $\frac{T}{2}$ is

$\frac{1}{2}$

$\frac{3}{4}$

$\frac{1}{\sqrt{2}}$

$\frac{\sqrt{2} - 1}{\sqrt{2}}$

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Explanation

$\frac{N}{N_{0}} = {(\frac{1}{2})}^{n} = {(\frac{1}{2})}^{t / T} ∴ \frac{N}{N_{0}} = {(\frac{1}{2})}^{\frac{T / 2}{T}} = {(\frac{1}{2})}^{1 / 2} = \frac{1}{\sqrt{2}}$

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If the decay or disintegration constant of a radioactive substance is $λ$ , then its half life and mean life are respectively

$\frac{1}{λ}$ and $\frac{\log_{e} 2}{λ}$

$\frac{\log_{e} 2}{λ}$ and $\frac{1}{λ}$

${λlog}_{e} 2$ and $\frac{1}{λ}$

$\frac{λ}{\log_{e} 2}$ and $\frac{1}{λ}$

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Explanation

(b) $H a l f l i f e = \frac{\log 2}{λ} M e a n l i f e = \frac{1}{λ}$

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Which of the following is in the increasing order for penetrating power

$α, β, γ$

$β, α, γ$

$γ, α, β$

$γ, β, α$

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Explanation

(a) Penetration power of $γ$ is 100 times of $β$ , while that of $β$ is 100 times of $α$ .

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The half life of a radioactive element which has only $\frac{1}{32}$ of its original mass left after a lapse of 60 days is

12 days

32 days

60 days

64 days

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Explanation

(a) $\frac{N_{0}}{32} = N_{0} {(\frac{1}{2})}^{60 / T} \Rightarrow 5 = \frac{60}{T} \Rightarrow T = 12 days$

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The half-life of ${Bi}^{210}$ is 5 days. What time is taken by (7/8)th part of the sample to decay

3.4 days

10 days

15 days

20 days

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Explanation

(c) By using $N = N_{0} {(\frac{1}{2})}^{t / T}$ where $N = (1 - \frac{7}{8}) N_{0} = \frac{1}{8} N_{0}$
So $\frac{1}{8} N_{0} = N_{0} {(\frac{1}{2})}^{t / T} \Rightarrow {(\frac{1}{2})}^{3} = {(\frac{1}{2})}^{t / 5} \Rightarrow t = 15 days$

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Radioactivity is

Irreversible process

Self disintegration process

Spontaneous process

All of the above

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Explanation

(d) All of the options apply for radioactivity.

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Half life of radioactive element depends upon

Amount of element present

Temperature

Pressure

Nature of element

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Explanation

(d) Half life of a substance doesn't depends upon Amount, temperature and pressure. It depends upon the nature of the substance.

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The decay constant of radium is $4.28 \times 10^{- 4}$ per year. Its half life will be

2000 years

1240 years

63 years

1620 years

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Explanation

(d) $T = \frac{0.6931 \times 1}{λ} = \frac{0.6931 \times 1}{4.28 \times 10^{- 4}} year = 1620 years$

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Which of the following is not a mode of radioactive decay

Positron emission

Electron capture

Fusion

Alpha decay

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Explanation

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