Ans.

(i)

Sol. Since both lasers have the same power, they both emit the same energy per second. But each violet photon carries more energy than a red photon, as explained below. Therefore, the red-light laser must emit more photons per second, in order to match the energy emitted by the violet-light laser.

To see why a red photon carries less energy than a violet photon, we can check the relationship between speed, wavelength, and frequency. v = λ f

This equation applies to all waves, not just electromagnetic waves. Solve for f to get f = So, since all wavelengths of light travel equally fast in a vacuum, wavelength and frequency are inversely proportional. Higher wavelengths correspond to lower frequencies.

Because red light waves are twice as long as violet light waves, red light has half the frequency of violet light. Since E = hf, each red photon carries half the energy of a violet photon. Therefore, as compared to the violet light laser, the red-light must emit twice as many photons per second, in order to produce the same energy.

(ii)

Sol. As just discussed, f = . Therefore, a photon carries energy E = hf = h

The photon energy is inversely proportional to the wavelength, λ . For instance, doubling λ cuts the energy in half. Tripling λ cuts the energy third. Only graph D captures this relationship. Graph c expresses a linear decrease, not an inverse proportionality.

(iii)

Sol. Since red light has a frequency of

f = = = 4.0 × 10 14 Hz,

a red photon carries an energy of

E = hf = (6.6 × 10 –34 J.s) (4.0 × 10 14 Hz) = 2.6 × 10 –19 J

Since all four choices differ by several orders of magnitude (e.g. 10 –28 joules is a billion times smaller than 10 –19 joules), PRECISE CALCULATIONS ARE UNNECESSARY. For instance, by using v = 10 8 m/s, λ = 10 –6 and h = 10 –34 J. s, you just need to add and subtract exponents. These numbers yield E = 10 –20 J, which unambiguously picks out option .