Chapter 19, Problem 7STP

Interpretation Introduction

Interpretation: The balanced nuclear equation of $Pa$ to produce a beta particle has to be written.

Concept introduction: The decay of nucleus by emitting a beta $\left({\text{e}}^{\text{-}}\right)$ particle is called as beta emission. In beta emission, one neutron of the original nucleus decays to form a beta particle and a proton. Due to which, the new nucleus formed has one more proton and one fewer neutron than the original nucleus.

The general equation is given as,

  $X\to e+Y$

Answer to Problem 7STP

The balanced nuclear equation for $Pa$ to produce a beta particle is,

  $Pa\to e+U$

Explanation of Solution

The decay of nucleus by emitting a beta $\left({\text{e}}^{\text{-}}\right)$ particle is called as beta emission. In beta emission, one neutron of the original nucleus decays to form a beta particle and a proton. Due to which, the new nucleus formed has one more proton and one fewer neutron than the original nucleus.

The general equation is given as,

  $X\to e+Y$

Where,

• $A$ is the mass number.
• $Z$ is the atomic number.
• $X$ is the original isotope.
• $Y$ is the new isotope.

Protactinium $\left(Pa\right)$ has an atomic number of $\text{91}$ and mass number $\text{234}\text{.}$

Mass number: Since a beta particle does not have any mass, the masses of the new particle and the original particle are $\text{234}\text{.}$

Atomic number: Since beta emission converts a neutron to a proton, the new nucleus formed will have one more proton than the original nucleus, $\text{91=-1+x}\text{.}$ Therefore, the atomic number of newly formed nucleus will be $\text{92}\text{.}$

From the periodic table, the element with atomic number of $92$ is identified as uranium.

Protactinium $\left(Pa\right)$ undergoes beta emission to form a beta particle and uranium whose atomic number is $\text{92}$ and mass number $\text{234}\text{.}$ The balanced nuclear equation is written as,

  $Pa\to e+U$

Conclusion

In beta emission, the atomic number of the original isotope is increased by one to form a new isotope and the mass number remains the same. The balanced nuclear equation for $Pa$ to produce a beta particle is,

  $Pa\to e+U$