Question

calculate the wavelength(1/m), frequency(hz),and energy(kj/mol) of visible light of wavelength 400
nm.

Answer 1

Question #41307 – Chemistry – Organic Chemistry

Question:

Calculate the wavelength (1/m), frequency (hz) and energy (kJ/mol) of visible light of wavelength 400 nm.

Answer:

To calculate all this values we will use the next formulas:

$$E = h v, \quad v = c / \lambda$$

where $E$ is for energy in J, $h$ is for the Plank’s constant ($h = 6,63 \cdot 10^{-34}$ J·s), $v$ is for the light frequency in Hz, $c$ is for the speed of light ($3 \cdot 10^{8}$ m/s) and $\lambda$ is for the wavelength of the light in meters.

1) Wavelength in 1/m.

$$1/400 \, \text{nm} = 1/400 \cdot 10^{-9} \, \text{m} = 1/4 \cdot 10^{-7} \, \text{m} = 0.25 \cdot 10^{7} \, \text{1/m} = 2.5 \cdot 10^{6} \, \text{m}^{-1}$$

2) Frequency $v$ in Hz.

$$v = c / \lambda = (3 \cdot 10^{8} \, \text{m/s}) / (4 \cdot 10^{-7} \, \text{m}) = 0.75 \cdot 10^{15} \, \text{Hz} = 7.5 \cdot 10^{14} \, \text{Hz}$$

3) Energy in kJ/mol.

$$E = h v = 6,63 \cdot 10^{-34} \, \text{J} \cdot \text{s} \cdot 7.5 \cdot 10^{14} \, \text{Hz} = 49.725 \cdot 10^{-20} \, \text{J} = 4.9725 \cdot 10^{19} \, \text{J} = 4.9725 \cdot 10^{16} \, \text{kJ}$$

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