A beam of light consists of a continuous range of wavelengths from 420 nm to 740 nm.

Question 6

A beam of light consists of a continuous range of wavelengths from 420 nm to 740 nm.

The light passes through a cloud of cool gas, as shown in Fig. 11.1.

Fig. 11.1

(a) The spectrum of the light emerging from the cloud of cool gas is viewed using a diffraction grating.

Explain why this spectrum contains a number of dark lines. [4]

(b) Some of the electron energy levels of the atoms in the cloud of gas are represented in Fig. 11.2.

Fig. 11.2 (not to scale)

(i) Light of wavelength 420 nm has a photon energy of 2.96 eV.

Calculate the photon energy, in eV, of light of wavelength 740 nm. [2]

(ii) Use data from (i) and your answer in (i) to show, on Fig. 11.2, the changes in energy

levels giving rise to the dark lines in (a). [2]

[Total: 8]

Reference: Past Exam Paper – June 2017 Paper 41 & 43 Q11

Solution:

(a)

The electrons (in the gas atoms/molecules) interact with the photons.

The photon energy (absorbed) causes the electron (to be excited and) to move to higher energy levels.

The photon energy absorbed is equal to the difference in energy of the (electron) energy levels.

When the electrons de-excite, photons are emitted in all directions (and so, this accounts for the dark lines).

(b)

(i)

EITHER

photon energy ∝ 1 /λ

{420 nm - - > 2.96 eV

1 nm - - > 2.96 × 420

740 nm - - > 2.96 × 420 / 740 = 1.68 eV}

energy = 1.68 eV       

OR

E = hc / λ

E = 6.63×10^-34 × 3.0×10⁸ / (740×10^-9)

E = 2.688 × 10^-19 J

{Energy in eV = 2.688×10^-19 / 1.6×10^-19 }

energy = 1.68 eV

(ii)

3.4 eV → 1.5 eV

3.4 eV → 0.85 eV

3.4 eV → 0.54 eV

{The wavelengths range from 420 nm to 740 nm.

As calculated above, the range for photon energy absorbed is from 1.68 eV (for 740 nm) to 2.96 eV. The changes in energy level cannot go beyond this range.

Starting from the -13.6 eV would give changes in energy that are too large (beyond the range).

Start from the -3.4 eV energy level.

Change in energy level = final level – initial level

3.4 eV → 1.5 eV         change = 3.4 – 1.5 = 1.9 eV

3.4 eV → 0.85 eV       change = 3.4 – 0.85 = 2.55 eV

3.4 eV → 0.54 eV       change = 3.4 – 0.54 = 2.86 eV

3.4 eV → 0.38 eV       change = 3.4 – 0.38 = 3.02 eV (beyond range)

So, only the 3 changes above correspond to the range. Starting from the other energy level would also be out of the range.}