A radioactive parent nucleus with an initial mass number of 226 undergoes a natural decay … — JAMB UTME

A radioactive parent nucleus with an initial mass number of $226$ undergoes a natural decay sequence in which it emits $3$ $\alpha$ -particles and $2$ $\beta^-$ -particles. What is the mass number of the resulting daughter nucleus?

Cevap: 214

Cevap

The mass number of the resulting daughter nucleus is 214.

Emitting an

\alpha

-particle reduces the nuclear mass number

A

4

, while emitting a

\beta^-

-particle leaves the mass number unchanged. Emitting

3

\alpha

-particles reduces the mass number by

3 \times 4 = 12

. Subtracting

12

from the original mass number of

226

yields a final mass number of

214

Adım Adım Çözüm

Identify the mass number change caused by alpha and beta emissions.

Each alpha particle decreases the mass number by 4, while each beta particle causes no change in mass number.

An alpha particle consists of 2 protons and 2 neutrons (mass number 4), whereas a beta particle is an electron with negligible mass in nucleon terms (mass number 0).

Calculate the total change in mass number.

Total mass number reduction = 3 * 4 = 12.

Three alpha particles are emitted in the decay sequence.

Calculate the mass number of the daughter nucleus.

Daughter mass number = 226 - 12 = 214.

Subtracting the total change in mass number from the original parent mass number.

Anahtar Kavram

Conservation of mass number in radioactive decay series

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