JEE Main · 2013 · 07 Apr 2013 · Offline · Atomic Structure

Energy of an electron is given by

E = - 2.178 \times 1 0^{- 18} \frac{Z ^{2}}{n ^{2}}

J. Wavelength of light required to excite an electron in an hydrogen atom from level

n = 1

n = 2

will be (

h = 6.62 \times 1 0^{- 34}

Js and

c = 3.0 \times 1 0^{8}

^{- 1}

)

Answer: (D)

Solution

The energy absorbed is the gap between the first two levels of hydrogen,

Δ E = 2.178 \times 1 0^{- 18} (\frac{1}{1 ^{2}} - \frac{1}{2 ^{2}}) = 2.178 \times 1 0^{- 18} \times \frac{3}{4} = 1.63 \times 1 0^{- 18} J

. The light that supplies this has wavelength

λ = \frac{h c}{Δ E} = \frac{( 6.62 \times 1 0 ^{- 34} ) ( 3.0 \times 1 0 ^{8} )}{1.63 \times 1 0 ^{- 18}} \approx 1.214 \times 1 0^{- 7} m

JEE Main · 2013 · 07 Apr 2013 · Offline · Single correct option