Nuclear Physics | Physics JEE previous year questions with Solutions

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Q 11 :

A radioactive element ${}_{92}^{242}X$ emits two $α$ -particles, one electron and two positrons. The product nucleus is represented by ${}_{P}^{234}Y$ . The value of $P$ is ________. [2023]

0%

(87)

$P = 92 - 2 - 2 + 1 - 1 - 1$

$P = 92 - 5$

$P = 87$

Q 12 :

A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is 30 s. The effective half-life of the nucleus is calculated to be $\frac{α}{11} s$ . The value of $α$ is _________. [2023]

0%

(300)

$\frac{d N_{1}}{d t} = - λ_{1} N$

$\frac{d N_{2}}{d t} = - λ_{2} N$

$\frac{d N}{d t} = - (λ_{1} + λ_{2}) N$

$\Rightarrow λ_{eq} = λ_{1} + λ_{2}$

$\Rightarrow \frac{1}{t_{1 / 2}} = \frac{1}{300} + \frac{1}{30} = \frac{11}{300}$

$\Rightarrow t_{1 / 2} = \frac{300}{11}$

Q 13 :

The decay constant for a radioactive nuclide is $1.5 \times 10^{- 5} s^{- 1}$ . Atomic of the substance is $60 {g mole}^{- 1}$ , $(N_{A} = 6 \times 10^{23})$ . The activity of $1.0 μ g$ of the substance is _________ $\times 10^{10} Bq$ . [2023]

0%

(15)

$λ = 1.5 \times 10^{- 5} s^{- 1}$

$Number of mole = \frac{1 \times 10^{- 6}}{60} = \frac{10^{- 7}}{6}$

$No. of atoms = no. of moles \times N_{A}$

$= \frac{10^{- 7}}{6} \times 6 \times 10^{23} = 10^{16}$

$A = N λ e^{- λ t}$

$For t = 0, A_{0} = N_{0} λ = 1.5 \times 10^{- 5} \times 10^{16} = 15 \times 10^{10} Bq$

Topic Question Set

Q 11 :

A radioactive element ${}_{92}^{242}X$ emits two $α$ -particles, one electron and two positrons. The product nucleus is represented by ${}_{P}^{234}Y$ . The value of $P$ is ________. [2023]

0%

Q 12 :

A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is 30 s. The effective half-life of the nucleus is calculated to be $\frac{α}{11} s$ . The value of $α$ is _________. [2023]

0%

Q 13 :

The decay constant for a radioactive nuclide is $1.5 \times 10^{- 5} s^{- 1}$ . Atomic of the substance is $60 {g mole}^{- 1}$ , $(N_{A} = 6 \times 10^{23})$ . The activity of $1.0 μ g$ of the substance is _________ $\times 10^{10} Bq$ . [2023]

0%

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