The electron energy in a hydrogen atom is given by `E_n = (-2.18 xx 10^(-18))//n^2 J`. Calculate the energy required to remove an electron completely from the `n=2` orbit. What is the longest wavelength of light in cm that can be used to cause this transition?

Options

A. `5.45xx10^(-19), 3. 647xx10^(-5)`
B. `2.48xx10^(-10), 4.851xx10^(-2)`
C. `6.54xx10^(-11), 6.682xx10^(-3)`
D. `8.52xx10^(-14), 9.822xx10^(-4)`

Answer

A

Explanation

Energy required to shift an electron from n = 2 to `n = oo`.
`DeltaE = E_(oo)– E_2 = 0 - (- (2.18xx10^(-18) J "atom"^(-1))/(2^2))`
`= 0.545xx10^(-18) J " atom"^(-1)`
`= 5.45xx10^(-19) J " atom"^(-1)`
Wavelength, `lambda = (hc)/(DeltaE)=(6.626xx10^(-34) Jsxx3.0xx10^8 ms^(-1))/( 5.45xx10^(-19))`
`=3.647xx10^(-7) m=3.647xx10^(-5) cm`.