Question

Confirm that charge, electron family number, and the total number of nucleons are all conserved by the rule for α decay given in the equation A Z XN → A − 4 Z − 2 YN − 2 + 4 2 He2. To do this, identify the values of each before and after the decay. (Use the following as necessary: Z and A.)

charge of A Z XN =

charge of A − 4 Z − 2 YN − 2 =

charge of 4 2 He2 =

electron family number of A Z XN =

electron family number of A − 4 Z − 2 YN − 2 =

electron family number of 4 2 He2 =

number of nucleons of A Z XN =

number of nucleons of A − 4 Z − 2 YN − 2 =

number of nucleons of 4 2 He2 =

Answer 1

In α decay, the total charge, electron family number, and the total number of nucleons before and after the decay are conserved. The initial nucleus loses two protons and two neutrons during the decay, and these are gained by the α particle (a Helium nucleus). Through this process, conservation laws are upheld.

Step-by-step explanation:

To verify that charge, electron family number, and the total number of nucleons are conserved in α decay, we need to look at each of these values before and after the decay. The initial nucleus AZXN decays into A-4Z-2YN-2 and an α particle, which is a 42He nucleus.

• Charge of AZXN = Z
• Charge of A-4Z-2YN-2 = Z-2
• Charge of 42He = 2
• Total charge conserved: Z = (Z-2) + 2
• Electron family number of AZXN = 0
• Electron family number of A-4Z-2YN-2 = 0
• Electron family number of 42He = 0
• Total electron family number conserved: 0 = 0 + 0
• Number of nucleons of AZXN = A
• Number of nucleons of A-4Z-2YN-2 = A-4
• Number of nucleons of 42He = 4
• Total nucleons conserved: A = (A-4) + 4

Thus, charge, electron family number, and the total number of nucleons are all conserved during α decay.