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

A radio isotope X has a half life of $10s$. Find the number of active nuclei in the sample (if initally there are $1000$ isotopes which are falling from rest from a height of $3000m$) when it is at a height of $1000m$ from the reference plane: 

  1. $50$
  2. $250$
  3. $29$
  4. $100$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Time taken in falling a height $h=3000-1000=2000m$ 

is given as $t=\sqrt[2]{\dfrac{2h}{g}}$
putting $g=10,h=2000$ we get $t=20second$
number of half life in this time period is $n=20/10=2$
So number of active nuclei$ = initial/2^n=initial/2^2=inital/4=1000/4=250$
Option B is correct.

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

When a $\beta^-$ particle is emitted from a nucleus, the neutron-proton ratio:

  1. is decreased

  2. is increased

  3. remains the same

  4. first (A) then (B)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$ _{A}^{Z}\textrm{X}$ $\rightarrow  _{A-1}^{Z}\textrm{Y} $  $+  \beta^{-1}$


So,  the neutron-proton ratio before emission $ = \dfrac{Z-A}{A}$

And, the neutron-proton ratio after emission $ = \dfrac{Z-A+1}{A-1}$
Since, $ \dfrac{Z-A+1}{A-1}$  $ >\dfrac{Z-A}{A}$
Therefore, B is correct option.

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

A certain mass of an ideal diatomic gas contained in a closed vessel is heated. It is observed that half the amount of gets dissociated, but the temperature remains constant. The ratio of the heat supplied to the gas to the initial internal energy of the gas will be

  1. $1:2$
  2. $1:4$
  3. $1:5$
  4. $1:10$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice physics nuclei beta decay change in nucleus due to radioactive decay alpha, beta and gamma particles (rays) and their properties

A positron is emitted by radioactive nucleus of proton number $90$. The product nucleus will have proton number :

  1. $91$
  2. $90$
  3. $89$
  4. $88$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The given nuclear reaction is-

$ _{90}X \rightarrow   _{+1}e $  $+ $ $ _zY$ 
Using law of conservation of atomic (or proton) number:
$90 = 1 + Z$
$\implies$ $Z = 89$
Thus the product nucleus will have proton number $89$.

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

When $ _{15}P^{30}$ decays to become  $ _{14}Si^{30}$, which particle is released ?

  1. electron
  2. $\alpha$-particle

  3. neutron

  4. positron
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The nuclear reaction :   $ _{15}P^{30}\rightarrow$   ${14}Si^{30} + $  $ _{+1}e^0$

Thus a positron is emitted during the decay of  $ _{15}P^{30}$ into   $ _{14}Si^{30}$.

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.