2019 A/L Physics Past Paper · Question 10 (English Medium)

Answer: (1) Only A

What the question asks

We want:

Which of the three statements about the laser are correct.

A: the laser acts between levels 2 and 1.

B: the pumping frequency is $\dfrac{E_3 - E_2}{h}$.

C: level 3 is the metastable level.

Relevant theory

In a three level system, Figure 8.8, the pumping radiation of frequency (E₃- E₁)/h, raises electrons from level 1 to level 3, from which they fall by spontaneous emission to level 2.

The laser action thus occurs between level 2 and 1 and the pumping radiation has different frequency from that of the stimulated radiation.

An inverted population can arise between level 2 and 1 if electrons remain long enough in level 2.

where h is the Planck constant and f the frequency of the absorbed photon.

A photon that is absorbed or given out between two levels has the energy:

$$\Delta E = hf$$

In a three-level laser:

Pumping: $1 \to 3$.

A quick fall: $3 \to 2$.

A long stay in level 2.

The laser light: $2 \to 1$.

Reading the options

The options list the statements that are correct.

Judge A, B and C first. Then pick the matching option.

Reasoning and calculation

Laser action between 2 and 1

Electrons fall from level 2 to level 1 by stimulated emission. A stream of photons comes out.

So the laser acts between levels 2 and 1.

The laser frequency is $\dfrac{E_2 - E_1}{h}$.

So A is correct.

A

Pumping frequency $\dfrac{E_3 - E_2}{h}$

The pumping photon lifts electrons from $E_1$ to level 3.

So its energy is $E_3 - E_1$. Its frequency is $\dfrac{E_3 - E_1}{h}$.

$\dfrac{E_3 - E_2}{h}$ would belong to the fall $3 \to 2$.

So B is wrong.

B

Level 3 is the metastable level

Level 3 is the pumping level.

The electrons do not stay there. They fall at once to level 2.

The metastable level is level 2.

So C is wrong.

C

B and C come from one mix-up.

The pumping level (3) and the metastable level (2) are swapped.

Pumping starts from the ground level.

The inverted population forms between the metastable level and the ground level.

Why the other options fail

It takes B to be correct and misses A.

C is wrong and A is missing.

C is wrong.

B and C are wrong and A is missing.

Conclusion

$f_{laser} = \frac{E_2 - E_1}{h},\quad f_{pump} = \frac{E_3 - E_1}{h}$

The laser acts between levels $2 \to 1$. So A is correct.

The pumping frequency is $\dfrac{E_3 - E_1}{h}$. So B is wrong.

The metastable level is level 2. So C is wrong.

So the answer is option (1).

Remember the three-level laser:

Pump $1 \to 3$.

Fall $3 \to 2$.

Stay in 2.

Laser light $2 \to 1$.

The pumping frequency and the laser frequency are always different.

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