Tag: physics

Questions Related to physics

The equation $ _{88}Ra^{226}\rightarrow _{86}Rn^{222}+ _{2}He^{4}$ emits which particle?

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. $\beta$-decay

  2. $\alpha$-decay

  3. $\gamma$-decay

  4. None of the above

Show answer
Correct Option: B
Explanation:

$\alpha $ - decay 

When an unstable atomic nucleus emits two protons and two neutrons the radioactive process is known as alpha decay. 

During $\beta^-$ emission:

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. a neutron in the nucleus decays emitting an electron

  2. an atomic electron is ejected

  3. an electron already present within the nucleus is ejected

  4. a part of the binding energy of the nucleus is converted into an electron

  5. a proton in the nucleus decays emitting an electron

Show answer
Correct Option: A
Explanation:

$\beta^-$ emission is due to decay of neutron in the nucleus $n\rightarrow p+e^-$.

Nuclei of a radioactive element $A$ are being produced at a constant rate $\alpha$. The element has a decay constant $\lambda$. At $t =0$, there are $N _{0}$ nuclei of the element.
If $\alpha = 2N _{0}\lambda$, calculate the number of nuclei of $A$ after one half life of $A$, and also the limiting value of $N$ as $t\rightarrow \infty$.

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. $\dfrac {4N _{0}}{2}, 2N _{0}$.

  2. $\dfrac {3N _{0}}{2}, 2N _{0}$.

  3. $\dfrac {5N _{0}}{2}, 2N _{0}$.

  4. $\dfrac {6N _{0}}{2}, 2N _{0}$.

Show answer
Correct Option: B

$90$% of a radioactive sample is left undecayed after time $t$ has elapsed. What percentage of the intial sample will decay in a total time $2t$:

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. $20$%

  2. $19$%

  3. $40$%

  4. $38$%

Show answer
Correct Option: B

$ _{84}P _{0}^{210}$ originally at rest emits $\alpha $- particles of KE 'K' Find  the KE of recoiling nucleus:

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. $\dfrac{4}{214}K$

  2. $\dfrac{4}{206}K$

  3. $\dfrac{K}{206}$

  4. $\dfrac{K}{214}K$

Show answer
Correct Option: B
Explanation:

$84P _o^{210}\xrightarrow 82Pb^{206}+\alpha \Rightarrow $ mass of remaining nucleus $(Pb)=206$

Initial momentum =$0$ (initial Po was at rest)
Momentum of $\alpha$- particle carrying $KE=K$
$P _1\sqrt{2m _{\alpha}k}$     $m _{alpha}=4n$,mass of $\alpha$
$P _1=\sqrt{8k}$
from conservation of momentum
$P _1+P _2=0$
$\Rightarrow P _1^2=P _2^2$
$2\ mrk'=2k$
$K'=\dfrac{4k}{mr}=\dfrac{4k}{206}$

When a radioactive nucleus emits a $\beta $- particular, the proton- neutron ratio

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. decreases

  2. increases

  3. remains same

  4. first decreases and increases

Show answer
Correct Option: B
Explanation:

When the neutron to proton ratio in the nucleus is too great a beta particle is emitted. In basic beta decay a neutron is transformed into a proton and an electron. The electron is then emitted as a beta particle which increases the atomic number by one and the molar mass is unchanged.

Hence, the proton- neutron ratio increase.

A free neutron is unstable against $\beta$ decay with a half life of about $600$ seconds:

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. The expression of this decay process in $n\rightarrow p+e^{-}+\vec{v}$

  2. If three are $600$ free neutrons initially, the time by which $450$ of them have decayed is $2400$ sec.

  3. The dacay rate of the sample is $0.593$ Bq.

  4. The dacay rate of the sample is $593$ Bq.

Show answer
Correct Option: C

Initial number of nuclei of a radioactive substance is $5 \times 10 ^ { 16 }$ and half-life is $10$ yrs. Find the number of nuclei decayed in $5$ yrs.

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. $2 \times 10 ^ { 16 }$

  2. $1.5 \times 10 ^ { 16 }$

  3. $3.5 \times 10 ^ { 16 }$

  4. $2.5 \times 10 ^ { 16 }$

Show answer
Correct Option: B
Explanation:

$Remaining$ nuclei after $5$ years will be $N=5\times 10^{16} \times (\dfrac{1}{2})^{5/10}=\dfrac{5\times 10^{16}}{\sqrt[2]{2}}=\dfrac{5\times 10^{16}}{1.414}=3.54\times 10^{16}$


So the decayed nuclei will be $(5-3.54)\times 10^{16}=1.46\times 10^{16}$
nearly $1.5\times 10^{16}$

A mixture consists of two radioactive materials ${ A } _{ 1 }$ and ${ A } _{ 2 }$ with half lives of 20 s and 10 s respectively. Initially the mixture has $40 g$ of ${ A } _{ 1 }$ and $160 g$ of ${ A } _{ 2 }$. The active amount of the two in the mixture will become equal after :

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. $20s$

  2. $40s$

  3. $60s$

  4. $80s$

Show answer
Correct Option: B

Samples of two radioactive nuclides $A$ and $B$ are taken. $\lambda _ { A }$ and $\lambda _ { B }$ are the disintegration constants of $A$ and $B$ respectively. In which of the following cases, the two samples can simultaneously have the same decay rate at any time ? 

physics nuclear physics beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

  1. Initial rate of decay of $A$ is twice the initial rate of decay of $B$ and $\lambda _ { A } = \lambda _ { B }$

  2. Initial rate of decay of $A$ is twice the initial rate of decay of $B$ and $\lambda _ { A } > \lambda _ { B }$

  3. Initial rate of decay of $B$ is twice the initial rate of decay of $A$ and $\lambda _ { A } > \lambda _ { B }$

  4. Initial rate of decay of $B$ is same as the rate of decay of $A$ at t = 2h and $\lambda _ { B } < \lambda _ { A }$

Show answer
Correct Option: A
Explanation:

$\begin{array}{l} N={ N _{ 0 } }{ e^{ -\lambda t } } \ \therefore if\, initial\, rate\, is\, same\, \, and\, { \lambda _{ A } }={ \lambda _{ B } } \end{array}$

Hence,
option $(A)$ is correct answer.