The radioactive isotope D decays according to the sequence $\mathrm{D} \xrightarrow{\;\beta^{-}\;} \mathrm{D}_{1} \xrightarrow{\;\alpha\;} \mathrm{D}_{2}$. If the mass number and atomic number of $\mathrm{D}_2$ are 176 and 71 respectively, what is (i) the mass number of D, (ii) the atomic number of D?

CBSE Class 12 · 2007 · Modern PhysicsVery Short Answer

The radioactive isotope D decays according to the sequence

D β^{-} D_{1} α D_{2}

. If the mass number and atomic number of

D_{2}

are 176 and 71 respectively, what is
(i) the mass number of D,
(ii) the atomic number of D?

Answer: Mass number $= 180$ , atomic number $= 72$ .

Work backwards from

D_{2} (A = 176, Z = 71)

.
Undo the

α

-emission (an

α

removes 4 from

A

and 2 from

Z

D_{1} : A = 176 + 4 = 180, Z = 71 + 2 = 73.

Undo the

β^{-}

-emission (

β^{-}

raises

Z

by 1, leaves

A

unchanged):

D : A = 180, Z = 73 - 1 = 72.

A_{D} = 180, Z_{D} = 72

CBSE Class 12 Board · 2007 · Subjective