Question

A radioactive nucleus emits 4 α-particles and 7 β-particles in succession. The ratio of number of neutrons of that of protons, is
[A = mass number, Z =atomic number]

Options

• `("A - Z - 13")/("Z - 2")`

• `("A - Z - 15")/("Z - 1")`

• `("A - Z - 13")/("Z - 1")`

• `("A - Z - 11")/("Z - 2")`

Answer 1

`("A - Z - 15")/("Z - 1")`

Explanation:

Let us assume, a particle X having atomic number Z and mass number A.

When an α-particle is emitted by a nucleus, then its atomic number decreases by 2 and mass number decreases by 4. So, for given case,

\[\ce{_ZX^A ->[4α-particle] _{Z - a}Y^{A - 16}}\]

When a β-particle is emitted by a nucleus its atomic number increases by one and mass number remains unchanged. So, for given case,

\[\ce{_{Z - 8}Y^{A - 16} ->[7β-particle] _{Z - 1}Z^{A - 16}}\]

∴ `"Number of neutrons"/"Number of protons" = (("A - 16") - ("Z - 1"))/(("Z - 1"))`

`= ("A - Z - 15")/(("Z - 1"))`