Question

A radioactive nucleus with \[Z\] protons and \[N\] neutrons emits an alpha particle, two beta-particles and two gamma rays. The number of protons and neutrons in the nucleus left after the decay respectively are
A. \[Z - 3;N - 1\]
B. \[Z - 1;N - 1\]
C. \[Z - 1;N - 3\]
D. \[Z;N - 4\]

Answer 1

Hint: In the given question, we have to determine the number of protons and neutrons in the nucleus left after the decay respectively. For this, we need to explain the process concept of the emission of alpha particles and beta particles.

Complete step by step solution:
We know that a radioactive nucleus with \[Z\] protons and \[N\] neutrons emit an alpha particle, two beta-particles and two gamma rays. So, we can say that with the emission of an alpha particle \[{}_2H{e^4}\] mass number decreases by forty four units. Also, its atomic number decreases by twenty two units and with emission of \[2{\beta ^{ - 1}}\;\] the particle's atomic number increases by twenty two units. Thus, \[Z\] will remain unchanged and \[N\] become \[N - 4\]. Thus, the number of protons and neutrons in the nucleus left after the decay respectively are \[Z\] and \[N - 4\] respectively.

Therefore, the correct option is D.

Additional Information: Beta radiation is the emission of electrons or positrons, and gamma radiation is the phrase used for the emission of powerful photons. Alpha radiation is the name for the emission of an alpha particle, which is actually a helium nucleus. A beta particle, also known as a beta ray or beta radiation (symbol ), is a highly energetic, swiftly moving electron or positron that is released during the radioactive disintegration of an atomic nucleus. Beta decay occurs in two ways: \[{\beta ^ + }\] decay and \[{\beta ^ - }\] decay, which results in the production of electrons and positrons, respectively.

Note: Many students make mistakes in writing explanations. They may explain only alpha emission. But it is essential to explain alpha and beta particle emission. Whenever a nucleus contains too many protons or neutrons, beta decay happens if one of the protons or neutrons is converted into the other.