Calculate the energy (in nJ) of a photon emitted by a mercury lamp with a frequency of 6.88 x 10¹⁴ Hz.

• 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

Answer: (D)

Verified step by step guidance

1. Start by recalling the formula for the energy of a photon, which is given by: $E=hf$, where $h$ is Planck's constant and $f$ is the frequency of the photon.
2. Planck's constant $h$ is approximately $6.626\times 10^-34$ J·s. Ensure you have this value ready for substitution into the formula.
3. Substitute the given frequency $6.88\times 10^14$ Hz into the formula: $E=6.626\times 10^-34\times 6.88\times 10^14$.
4. Calculate the energy in joules first. This involves multiplying the values of Planck's constant and the frequency. Remember to handle the powers of ten correctly during multiplication.
5. Convert the energy from joules to nanojoules (nJ) by multiplying the result by $10^9$, since 1 nJ = $10^-9$ J.