Calculate the energy of a photon emitted by a mercury lamp

What is the energy of a photon emitted by a mercury lamp with a frequency of 6.88 x 10¹⁴ Hz?

Options:

A. 5.46 x 10⁻⁹ nJ

B. 9.89 x 10⁻⁹ nJ

C. 2.89 x 10⁻¹⁰ nJ

D. 4.56 x 10⁻¹⁰ nJ

Final answer:

The correct option is D. The energy of the photon emitted by the mercury lamp with a frequency of 6.88 x 10¹⁴ Hz is approximately 4.56 x 10⁻¹⁰ nJ.

To calculate the energy of a photon emitted by a mercury lamp, we can use the equation:

E = hf

Where:

E is the energy of the photon

h is Planck's constant (6.626 x 10⁻³⁴ J·s)

f is the frequency of the photon

Given that the frequency of the photon emitted by the mercury lamp is 6.88 x 10¹⁴ Hz, we can substitute this value into the equation:

E = (6.626 x 10⁻³⁴ J·s) x (6.88 x 10¹⁴ Hz)

Calculating this expression gives us the energy of the photon in joules. To convert this to nanojoules, we can use the conversion factor 1 J = 10⁹ nJ:

E = (6.626 x 10⁻³⁴ J·s) x (6.88 x 10¹⁴ Hz)

E = 4.55648 x 10⁻¹⁹ J

Converting this to nanojoules:

E = 4.55648 x 10⁻¹⁹ J x 10⁹ nJ/J

E = 4.55648 x 10⁻¹⁰ nJ

Therefore, the energy of the photon emitted by the mercury lamp with a frequency of 6.88 x 10¹⁴ Hz is approximately 4.56 x 10⁻¹⁰ nJ.