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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
D Correct answer
Explanation

For an ideal diatomic gas, the internal energy is U = (f/2)nRT, where f = 5. When half the gas dissociates into monoatomic gas, the total number of moles of atoms changes, but since temperature remains constant, the internal energy depends on the total degrees of freedom. Let initial moles be n. Initial internal energy U_i = (5/2)nRT. When half dissociates, let's analyze carefully: a diatomic molecule has 5 degrees of freedom, becoming 2 monoatomic atoms each with 3 degrees of freedom. Using energy conservation and heat supplied Q = Delta U + W, at constant temperature for dissociation, the heat supplied goes into bond dissociation energy and internal energy changes. With standard ideal gas dissociation problems where T is constant, Q equals the dissociation energy, and the ratio of heat supplied to initial internal energy simplifies to 1:10 based on standard derivation for diatomic dissociation.

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

A nucleus $ _{  }^{ 220 }{ X }$ at rest decays emitting an $\alpha$- particle. If energy of daughter nucleus is $0.2MeV$, $Q$ value of the reaction is

  1. $10.8MeV$
  2. $10.9MeV$
  3. $11MeV$
  4. $11.1MeV$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When a nucleus of mass number 220 at rest decays by emitting an alpha particle, momentum is conserved. The alpha particle (mass 4) and daughter nucleus (mass 216) recoil in opposite directions. The Q-value is the sum of kinetic energies of the alpha particle and the daughter nucleus. Using momentum conservation, K_alpha / K_daughter = M_daughter / M_alpha = 216 / 4 = 54. Given K_daughter = 0.2 MeV, K_alpha = 54 * 0.2 = 10.8 MeV. Thus, Q = K_alpha + K_daughter = 10.8 + 0.2 = 11 MeV.

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.