JEE Main · 2014 · 06 Apr 2014 · Offline · Modern Physics

Hydrogen

(_{1} H^{1})

, Deuterium

(_{1} H^{2})

, singly ionised Helium

(_{2} He^{4})^{+}

and doubly ionised lithium

(_{3} Li^{6})^{++}

all have one electron around the nucleus. Consider an electron transition from

n = 2

n = 1

. If the wave lengths of emitted radiation are

λ_{1}, λ_{2}, λ_{3}

and

λ_{4}

respectively then approximately which one of the following is correct?

Answer: (A)

Solution

For a one-electron atom,

\frac{1}{λ} = R Z^{2} (\frac{1}{n _{1}^{2}} - \frac{1}{n _{2}^{2}})

, so for the

n = 2 \to 1

line

λ \propto \frac{1}{Z ^{2}}

. Hydrogen and deuterium both have

Z = 1

, so

λ_{1} = λ_{2}

. Singly ionised helium has

Z = 2

, making

λ_{3} = \frac{λ _{1}}{4}

, and doubly ionised lithium has

Z = 3

, making

λ_{4} = \frac{λ _{1}}{9}

. Reading these together,

λ_{1} = λ_{2} = 4 λ_{3} = 9 λ_{4}

JEE Main · 2014 · 06 Apr 2014 · Offline · Single correct option