Question

Write balanced equations that represent the following nuclear reaction.

1. Alpha emission by ${}_{70}{}^{155}\mathbf{Yb}$
2. Positron emission by${}_{14}{}^{26}\mathbf{Si}$
3. Electron capture${}_{30}{}^{65}\mathbf{Zn}$
4. Electron emission by ${}_{41}{}^{100}\mathbf{Nb}$

Short answer

The balanced nuclear reactions are given below.

1. ${}_{70}{}^{155}\mathrm{Yb}\to {}_{68}{}^{151}\mathrm{Er}+{}_2{}^4\mathrm{He}$
2. ${}_{14}{}^{26}\mathrm{Si}\to {}_{13}{}^{26}\mathrm{Al}+{}_1{}^0\mathrm{e}^{+}+\mathrm{\nu }$
3. ${}_{30}{}^{65}\mathrm{Zn}+{}_{-1}{}^0\mathrm{e}^{-}\to {}_{29}{}^{65}\mathrm{Cu}+\mathrm{\nu }$
4. ${}_{41}{}^{100}\mathrm{Nb}\to {}_{42}{}^{100}\mathrm{Mo}+{}_{-1}{}^0\mathrm{e}^{-}+\overline{\mathrm{\nu }}$

Step-by-step solution

Alpha emission

An alpha particle is a doubly ionized Helium atom. It is represented as ${}_2{}^4\text{He}$. When an alpha particle is emitted, the mass number of the daughter nucleus decreases by 4 and the atomic number decreases by 2.

The balanced nuclear reaction representing alpha emission by data-custom-editor="chemistry" ${}_{70}{}^{155}\text{Yb}$is:

${}_{70}{}^{155}\mathrm{Yb}\to {}_{68}{}^{151}\mathrm{Er}+{}_2{}^4\mathrm{He}$

Positron Emission

When the number of protons is more than the number of neutrons in a nucleus, positron emission takes place to stabilize the nucleus. In a positron emission, a proton is transformed to a neutron along with the emission of a high energy positron accompanied by a neutrino. No change in mass number is observed for a positron emission. The atomic number of the daughter nucleus is one less than that of the parent nucleus.

The balanced nuclear reaction representing positron emission by${}_{14}{}^{26}\text{Si}$ is:

${}_{14}{}^{26}\mathrm{Si}\to {}_{13}{}^{26}\mathrm{Al}+{}_1{}^0\mathrm{e}^{+}+\mathrm{\nu }$

Electron capture

In this process, an electron is captured by the nucleus and a proton is transformed into a neutron. No change in mass number is observed and the atomic number of the daughter nucleus is decreased by 1 unit. A neutrino emission occurs in this process.

The balanced nuclear reaction representing the electron capture by${}_{30}{}^{65}\text{Zn}$ is:

${}_{30}{}^{65}\mathrm{Zn}+{}_{-1}{}^0\mathrm{e}^{-}\to {}_{29}{}^{65}\mathrm{Cu}+\mathrm{\nu }$

Electron emission

When the number of neutrons is more than the number of protons in a nucleus, electron emission takes place to stabilize the nucleus. Electron emission is also known as $\mathrm{\beta }$decay. When electron emission takes place, a neutron is converted to a proton and a high energy electron. This high energy electron is known as$\mathrm{\beta }$ particle. There is no change in the mass number when electron emission takes place. The atomic number of the daughter nucleus increases by 1.

The balanced nuclear reaction representing electron emission by ${}_{41}^{100}\text{Nb}$is:

${}_{41}{}^{100}\mathrm{Nb}\to {}_{42}{}^{100}\mathrm{Mo}+{}_{-1}{}^0\mathrm{e}^{-}+\overline{\mathrm{\nu }}$