QuestionJune 26, 2025

Which of the following photons has the highest energy? a) a photon with lambda =647nm b) a photon with lambda =633pm c) a photon with lambda =1.064mu m d) a photon with v=1.55times 10^15Hz e) a photon with v=5.83times 10^14Hz

Which of the following photons has the highest energy? a) a photon with lambda =647nm b) a photon with lambda =633pm c) a photon with lambda =1.064mu m d) a photon with v=1.55times 10^15Hz e) a photon with v=5.83times 10^14Hz
Which of the following photons has the highest energy?
a) a photon with lambda =647nm
b) a photon with lambda =633pm
c) a photon with lambda =1.064mu m
d) a photon with v=1.55times 10^15Hz
e) a photon with v=5.83times 10^14Hz

Solution
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Answer

Option d) a photon with v=1.55\times 10^{15}Hz has the highest energy. Explanation 1. Identify the Energy Formula The energy of a photon is given by **E = \frac{hc}{\lambda}** or **E = hv**, where h is Planck's constant and c is the speed of light. 2. Calculate Energy for Each Option a) \lambda = 647 \, \text{nm} = 647 \times 10^{-9} \, \text{m}: E_a = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{647 \times 10^{-9}} b) \lambda = 633 \, \text{pm} = 633 \times 10^{-12} \, \text{m}: E_b = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{633 \times 10^{-12}} c) \lambda = 1.064 \, \mu \text{m} = 1.064 \times 10^{-6} \, \text{m}: E_c = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{1.064 \times 10^{-6}} d) v = 1.55 \times 10^{15} \, \text{Hz}: E_d = 6.626 \times 10^{-34} \times 1.55 \times 10^{15} e) v = 5.83 \times 10^{14} \, \text{Hz}: E_e = 6.626 \times 10^{-34} \times 5.83 \times 10^{14} 3. Compare Energies Calculate each energy value to determine which is highest.

Explanation

1. Identify the Energy Formula<br /> The energy of a photon is given by **$E = \frac{hc}{\lambda}$** or **$E = hv$**, where $h$ is Planck's constant and $c$ is the speed of light.<br /><br />2. Calculate Energy for Each Option<br /> a) $\lambda = 647 \, \text{nm} = 647 \times 10^{-9} \, \text{m}$: $E_a = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{647 \times 10^{-9}}$<br /> b) $\lambda = 633 \, \text{pm} = 633 \times 10^{-12} \, \text{m}$: $E_b = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{633 \times 10^{-12}}$<br /> c) $\lambda = 1.064 \, \mu \text{m} = 1.064 \times 10^{-6} \, \text{m}$: $E_c = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{1.064 \times 10^{-6}}$<br /> d) $v = 1.55 \times 10^{15} \, \text{Hz}$: $E_d = 6.626 \times 10^{-34} \times 1.55 \times 10^{15}$<br /> e) $v = 5.83 \times 10^{14} \, \text{Hz}$: $E_e = 6.626 \times 10^{-34} \times 5.83 \times 10^{14}$<br /><br />3. Compare Energies<br /> Calculate each energy value to determine which is highest.
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