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.