Question

N
z?
Wavelength of light required to excite
5.
Energy of an electron is given by E= -2.178 x 10 18
n
an electron in an hydrogen atom from level n = 1 to n = 2 will be
(n = 6.62 x 10 34 Js and c = 3.0 10 ms )
(1) 2.816 x 10 m
(2) 6.500 x 10m
(3) 8.500 , 10m
(4) 1.214 x 10-'m
(MAINS-2013)​

Answer 1

QUESTION:

Energy of an electron is given

$E = - 2.178 \times {10}^{ - 18}( \frac{1}{ {n2}^{2} } - \frac{1}{ {n1}^{2} })$

an electron in an hydrogen atom from level

n 1 = 1 to n 2 = 2 will be

(h = 6.62 x 10^- 34 Js and c = 3.0 ×10 ^8m/s ).

SOLUTION

Energy of the electron in an hydrogen atom is given as ,

E

$E = - 2.178 \times {10}^{ - 18}( \frac{1}{ {n2}^{2} } - \frac{1}{ {n1}^{2} })$

$E = - 2.178 \times {10}^{ - 18}( \frac{1}{ 4} - \frac{1}{ 1 })$

$E = - 2.178 \times {10}^{ - 18}( \frac{ - 3}{ 4} )$

$E = 1.6335 \times {10}^{ - 18}$

We know that ,

$E = \frac{hc}{ \lambda}$

$\lambda = \frac{hc }{E }$

$\lambda = \frac{6.6 \times {10}^{ - 34} \times 3 \times {10}^{8} }{1.6335 \times {10}^{ - 18} }$

$\lambda =12.12 \times {10}^{ - 8} m$

$\boxed{ \lambda =1.212 \times {10}^{ - 7} m}$