Energy of an electron is givem by `E = - 2.178 xx 10^-18 J ((Z^2)/(n^2))`. Wavelength of light required to excited an electron in an hydrogen atom from level `n = 1` to `n = 2` will be
`(h = 6.62 xx 10^-34 Js` and `c = 3.0 xx 10^8 ms^-1`).

Options

A. `8.500 xx 10^(-7)m`
B. `1.214 xx 10^(-7) m`
C. `2.816 xx 10^(-7) m`
D. `6.500 xx 10^(-7) m`

Answer

B

Explanation

`E_1 = -2.178 xx 10^(-18) xx (1^2)/(1^2) = -2.178 xx 10^(-18) J`
`E_2 = -2.178 xx 10^(-18) xx (1^2)/(2^2) = -5.445 xx 10^(-19)J`
Energy required to excite electron from `n = 1` to `n = 2`,
`DeltaE = -5.445 xx 10^(-19) - (-2.178 xx 10^(-18))`
`= 16.335 xx 10^(-19) J`
`(hc)/(lambda) = 16.335 xx 10^(-19)`
`lambda = (6.63 xx 10^(-34) xx 3.0 xx 10^8)/(16.335 xx 10^(-19))`
`= 1.217 xx 10^(-7)m`.