Consider the following radioactive decay process ${ }_{84}^{218} A \xrightarrow{\alpha} A_1 \xrightarrow{\beta^{-}}A_2 \xrightarrow{\gamma} A_3 \xrightarrow{\alpha} A_4 \xrightarrow{\beta^{+}} A_5 \xrightarrow{\gamma}A_6$ The mass number and the atomic number of $A_6$ are given by:

Question

The average energy released per fission for the nucleus of $^{235_{92}U$ is 190 MeV. When all the atoms of 47 g pure $^{235}_{92}U$ undergo fission process, the energy released is $\alpha \times 10^{23}$ MeV. The value of $\alpha$ is ___. (Avogadro Number $= 6 \times 10^{23}$ per mole)}

Answer 1

To determine the mass number and the atomic number of $ A_6 $ in the given radioactive decay process, we need to understand each type of decay and how it affects the nucleus.

${ }_{84}^{218} A \xrightarrow{\alpha} A_1$: An alpha ($ \alpha $) particle consists of 2 protons and 2 neutrons. Thus, during an alpha decay, the atomic number decreases by 2, and the mass number decreases by 4.
- Atomic Number: $ 84 - 2 = 82 $
- Mass Number: $ 218 - 4 = 214 $
$A_1 \xrightarrow{\beta^{-}} A_2$: In beta-minus ($ \beta^- $) decay, a neutron is converted into a proton, increasing the atomic number by 1 while the mass number remains unchanged.
- Atomic Number: $ 82 + 1 = 83 $
- Mass Number: $ 214 $
$A_2 \xrightarrow{\gamma} A_3$: Gamma ($ \gamma $) decay does not change the atomic number or the mass number, as it is purely an energy release.
- Atomic Number: $ 83 $
- Mass Number: $ 214 $
$A_3 \xrightarrow{\alpha} A_4$: Another alpha decay reduces both atomic and mass numbers as before.
- Atomic Number: $ 83 - 2 = 81 $
- Mass Number: $ 214 - 4 = 210 $
$A_4 \xrightarrow{\beta^{+}} A_5$: In beta-plus ($ \beta^+ $) decay, a proton is converted into a neutron, decreasing the atomic number by 1 while the mass number remains unchanged.
- Atomic Number: $ 81 - 1 = 80 $
- Mass Number: $ 210 $
$A_5 \xrightarrow{\gamma} A_6$: Again, gamma decay doesn't affect the atomic or mass numbers.
- Atomic Number: $ 80 $
- Mass Number: $ 210 $

Hence, the mass number and the atomic number of $ A_6 $ are 210 and 80, respectively.

The correct answer is:

210 and 80

Consider the following radioactive decay process ${ }_{84}^{218} A \xrightarrow{\alpha} A_1 \xrightarrow{\beta^{-}}A_2 \xrightarrow{\gamma} A_3 \xrightarrow{\alpha} A_4 \xrightarrow{\beta^{+}} A_5 \xrightarrow{\gamma}A_6$ The mass number and the atomic number of $A_6$ are given by:

The Correct Option is B

Solution and Explanation

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