Chapter U1.15, Problem 7E

Interpretation Introduction

Interpretation:

Isotope name and symbol of new element formed due to beta emission of given isotopes have to be determined and also their stability has to be predicted from isotope graph.

Concept introduction:

Unstable elements can be changed to new elements by emitting subatomic particles. When electrons are emitted from nucleus of an atom, it is called beta decay. The emitted electron is called beta particle.

Answer to Problem 7E

The following table shows isotope name and symbol of new element formed due to beta emission.

Element	New isotope formed	symbol	stability
Potassium - 42	Calcium-42	${}_{20}^{42}\text{Ca}$	✓
Iodine - 131	Xenon-131	${}_{54}^{131}\text{Xe}$	✓
Iron - 52	Cobalt-52	${}_{27}^{52}\text{Co}$
Sodium - 24	Magnesium-24	${}_{12}^{24}\text{Mg}$	✓

Explanation of Solution

Given information: The following isotopes of elements are given.

Potassium - 42, Iodine - 131, Iron - 52, Sodium - 24

From the periodic table we get to know the atomic number of elements.

1. Potassium - 42 - Atomic number of potassium is 19. During beta decay, a neutron splits into a proton and an electron. So the number of protons increase by one and number of neutrons decrease by one in the nucleus. The atomic mass however remains the same as mass of proton and neutron is almost same, but the atomic number increases by one. So the atomic number of new atom becomes 20, and the mass number remains same. The new isotope with 20 as atomic number is calcium. It is a stable atom.
The equation for this is:

${}_{19}^{42}K{\to }_{20}^{40}Ca+\beta$

2. Iodine - 131 - Atomic number of iodine is 53. During beta decay, a neutron splits into a proton and an electron. So the number of protons increase by one and number of neutrons decrease by one in the nucleus. The atomic mass however remains the same as mass of proton and neutron is almost same, but the atomic number increases by one. So the atomic number of new atom becomes 54, and the mass number remains same. The new isotope with 20 as atomic number is xenon. It is a stable atom.
The equation for this is:

${}_{53}^{131}I{\to }_{54}^{131}Xe+\beta$

3. Iron - 52 - Atomic number of iron is 26. During beta decay, a neutron splits into a proton and an electron. So the number of protons increase by one and number of neutrons decrease by one in the nucleus. The atomic mass however remains the same as mass of proton and neutron is almost same, but the atomic number increases by one. So the atomic number of new atom becomes 27, and the mass number remains same. The new isotope with 27 as atomic number is cobalt. It is not a stable atom.
The equation for this is:

${}_{26}^{52}Fe{\to }_{27}^{52}Co+\beta$

4. Sodium - 24 - Atomic number of sodium is 11. During beta decay, a neutron splits into a proton and an electron. So the number of protons increase by one and number of neutrons decrease by one in the nucleus. The atomic mass however remains the same as mass of proton and neutron is almost same, but the atomic number increases by one. So the atomic number of new atom becomes 12, and the mass number remains same. The new isotope with 12 as atomic number is magnesium. It is a stable atom.
The equation for this is:

${}_{11}^{24}Na{\to }_{12}^{24}Mg+\beta$

Conclusion

Beta decay causes the atomic number to increase by one so one move one space forward in the periodic table.