Tag: change in nucleus due to radioactive decay

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

What would be an atom that has lost an electron?

  1. Positron

  2. Negatron

  3. Baryon

  4. Hadron

  5. Ion
Reveal answer Fill a bubble to check yourself
E Correct answer
Explanation

We know that an atom is electrically neutral because it has equal number of electrons(negative charge) and protons(positive charge) , now when it has lost an electron , negative charge decreases in the atom hence the net charge is now positive, the atom would be an ion.

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

For which of the following events will the resulting products have more mass than the mass of the stuff from which the products came?

  1. Alpha decay

  2. Beta decay

  3. An exothermic nuclear reaction

  4. An endothermic nuclear reaction

  5. Nuclear fission of uranium $-235$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In an endothermic nuclear reaction, heat energy is given to the reaction to proceed and thus according to Einstein's mass-energy equivalence law, heat energy given gets converted into additional mass which results in the formation of products with more mass than the reactants.

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

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

  1. $\beta$-decay

  2. $\alpha$-decay

  3. $\gamma$-decay

  4. None of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\alpha $ - decay 

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

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

During $\beta^-$ emission:

  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
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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

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

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 $t\rightarrow \infty$.

  1. <span>$\dfrac {4N _{0}}{2}, 2N _{0}$.</span>

  2. <span>$\dfrac {3N _{0}}{2}, 2N _{0}$.</span>

  3. <span>$\dfrac {5N _{0}}{2}, 2N _{0}$.</span>

  4. <span>$\dfrac {6N _{0}}{2}, 2N _{0}$.</span>
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The rate equation is dN/dt = alpha - lambda*N. Solving this with N(0)=N0 and alpha=2*N0*lambda leads to N(t) = 2*N0 - N0*exp(-lambda*t). At t = half-life (ln2/lambda), N = 2*N0 - N0/2 = 1.5*N0. As t approaches infinity, N approaches 2*N0.

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

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

  1. $20$%

  2. $19$%

  3. $40$%

  4. $38$%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

After time t, 90% remains (N/N0 = 0.9). After time 2t, the fraction remaining is (0.9)^2 = 0.81. The amount decayed is 1 - 0.81 = 0.19, or 19%.

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

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

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

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

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

  4. $\dfrac{K}{214}K$
Reveal answer Fill a bubble to check yourself
B Correct answer
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
$P _1+P _2=0$
$\Rightarrow P _1^2=P _2^2$
$2\ mrk'=2k$
$K'=\dfrac{4k}{mr}=\dfrac{4k}{206}$

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

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

  1. decreases

  2. increases

  3. remains same

  4. first decreases and increases
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  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.
Reveal answer Fill a bubble to check yourself
C Correct answer