Q33PE - College Physics (Urone)

Question

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for electron capture given in theequation \(_Z^A{X_N} + {e^ - } \to _{Z - 1}^A{Y_{N + 1}} + {v_e}\). To do this, identify the values of each before and after the capture.

Step-by-Step Solution

Answer

The electron numbers and the nucleons numbers are conserved.

Define Radioactivity

The spontaneous emission of radiation in the form of particles or high-energy photons as a result of a nuclear process is known as radioactivity.

Confirmation that the charges are preserved

The reaction we have is:

\(_Z^A{X_N} + {e^ - } \to _{Z - 1}^A{Y_{N + 1}} + {v_e}\)

The value X has a charge of + Z.

The value of e^- has a charge of - 1.

The total charge prior to capture is Z - 1.

The value of Y has a charge of Z - 1.

The charge on v_e is zero.

The charge following the reaction is Z - 1.

As a result, the reaction's charge is preserved.

 

Identifying the values before and after capture

The electron number of X is zero, while that of e^- is one. 

The electron number before the process is 1.

The number of electrons in Y is zero, but the number of electrons in v^e is one. 

Following the process, the electron number is 1.

The reaction's electron number is preserved.

The number of nucleons in X is A, and e^-  is zero. 

The number of nucleons before the reaction is A.

The number of nucleons in Y is A, and v^e is zero. 

The nucleon number following the reaction is A.

The number of nucleons in the process is preserved.

Therefore, the electron and nucleon numbers are preserved.