QuestionJune 27, 2025

Calculate the frequency of the green light emitted by a hydrogen atom with a wavelength of 486.1 nm. 6.86times 10^14J 4.09times 10^-19J 4.33times 10^14J 4.86times 10^-7J

Calculate the frequency of the green light emitted by a hydrogen atom with a wavelength of 486.1 nm. 6.86times 10^14J 4.09times 10^-19J 4.33times 10^14J 4.86times 10^-7J
Calculate the frequency of the green light emitted by a hydrogen atom with a wavelength of 486.1 nm. 6.86times 10^14J 4.09times 10^-19J 4.33times 10^14J 4.86times 10^-7J

Solution
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Answer

6.17 \times 10^{14} \, \text{Hz} Explanation 1. Identify the formula for frequency Use the formula **c = \lambda \cdot f**, where c is the speed of light (3 \times 10^8 \, \text{m/s}), \lambda is the wavelength, and f is the frequency. 2. Convert wavelength to meters Convert 486.1 nm to meters: 486.1 \, \text{nm} = 486.1 \times 10^{-9} \, \text{m}. 3. Solve for frequency Rearrange the formula to find frequency: f = \frac{c}{\lambda}. Substitute c = 3 \times 10^8 \, \text{m/s} and \lambda = 486.1 \times 10^{-9} \, \text{m}. Calculate: f = \frac{3 \times 10^8}{486.1 \times 10^{-9}} \approx 6.17 \times 10^{14} \, \text{Hz}.

Explanation

1. Identify the formula for frequency<br /> Use the formula **$c = \lambda \cdot f$**, where $c$ is the speed of light ($3 \times 10^8 \, \text{m/s}$), $\lambda$ is the wavelength, and $f$ is the frequency.<br /><br />2. Convert wavelength to meters<br /> Convert 486.1 nm to meters: $486.1 \, \text{nm} = 486.1 \times 10^{-9} \, \text{m}$.<br /><br />3. Solve for frequency<br /> Rearrange the formula to find frequency: $f = \frac{c}{\lambda}$. Substitute $c = 3 \times 10^8 \, \text{m/s}$ and $\lambda = 486.1 \times 10^{-9} \, \text{m}$.<br /> Calculate: $f = \frac{3 \times 10^8}{486.1 \times 10^{-9}} \approx 6.17 \times 10^{14} \, \text{Hz}$.
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