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# After the emission of one $\alpha$ - particle followed by two $\beta$ - particles from $U_{92}^{238}$ the number of neutrons in the newly formed nucleus is:A) $140$B) $142$C) $144$D) $146$

Last updated date: 18th Sep 2024
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Hint: Write the chemical formula of the disintegration of the uranium and from that find the mass number and the atomic number of the newly formed nucleus. Subtract the obtained mass number and the atomic number to obtain the number of neutrons.

Useful formula:
(1) The number of neutrons is given by
$n = A - Z$
Where $n$ is the number of neutrons, $A$ is the mass number of the molecule and the $Z$ is the atomic number.

Complete step by step solution:
The chemical reactions of the emission of the $\alpha$ particle and the $\beta$ - particles from $_{92}^{238}U$ is given by
$_{92}^{238}U \to _2^4He + _{ - 1}^0e + _Z^AX$
The mass number of the reaction, $A = 238 - 4 + 0$
By performing the basic arithmetic operation,
$A = 234$
The number of protons of the unknown chemical product is calculated by subtracting the number of protons of the product and number of protons of the reactant.
The number of protons, $Z = 92 - 2 + 1$
By performing the basic arithmetic operation in the above step.
$Z = 92$
The number of neutrons can be found by subtracting the number of protons from the mass number.
Number of neutrons= $A - Z$
By substituting the known values in the above equations,
Number of neutrons= $234 - 92$
By subtracting the values in the right hand side of the equation.
Number of neutrons= $142$
Hence the number of neutrons in the newly formed nucleus is calculated as $142$ .

Thus the option (B) is correct.

Note: The top number of any substance specifies the mass number of the molecule. It is the sum of the number of the protons and the number of neutrons. The number that is located at the bottom of the molecule species is the number of protons.