Question

Calculate the wavelength (in nanometers) of a photon emitted by a hydrogen atom when its electron drops from the n = 4 to n = 2 state.

**Consider the following energy levels of a hypothetical
atom:**

*E*_{4} **−1.61** ×
**10**^{−19} **J**

*E*_{3} **−7.51** ×
**10**^{−19} **J**

*E*_{2} **−1.35** ×
**10**^{−18} **J**

*E*_{1} **−1.45** ×
**10**^{−18} **J**

**(a) What is the wavelength of the photon needed to
excite an electron from** *E*_{1}
**to** *E*_{4}**?**

____ ×**10****m**

**(b) What is the energy (in joules) a photon must have in
order to excite an electron from** *E*_{2}
**to** *E*_{3}**?**

**___**× **10****J**

**(c) When an electron drops from the**
*E*_{3} **level to the**
*E*_{1} **level, the atom is said to undergo
emission. Calculate the wavelength of the photon emitted in this
process.**

**___**×**10** **m**

Answer #1

a) ∆E =E_{4} **-** E_{1} = −1.61 ×
10^{−19} J - (−1.45 × 10^{−18} J ) =
1.289x10^{−18} J

∆E = hc/ λ = ( 6.625x10^{-34}Js x
3x10^{8}ms^{-1}) / (1.289x10^{−18} J) =
**15.41 x 10 ^{-8} m = 154 nm**

The photon needed to excite an electron from E_{1} to
E_{4} is 154 nm

b) ∆E =E2 **-** E3 = −1.35 × 10^{−18} J -
(−7.51 × 10^{−19} J ) = 0.599x10^{−18} J **=
5.99x10 ^{−19} J**

The energy (in joules) a photon must have in order to excite an
electron from E2 to E3 is 5.99x10^{−19} J

**c)** ∆E =E1 - E3 = −1.45 × 10^{−18} J -
(−7.51 × 10^{−19} J ) = 0.699x10^{−18} J

∆E = hc/ λ = (6.625x10^{-34}Js x
3x10^{8}ms^{-1}) / (0.699x10^{−18} J) =
**28.4 x 10 ^{-8} m = 284 nm**

The wavelength of the photon emitted in this process is 284 nm

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