Question

Heated lithium atoms emit photons of light with an energy of 2.961 × 10^−19 J. Calculate the frequency and wavelength of one of these photons. What is the total energy in 1 mole of these photons? What is the color of the emitted light?

a) Frequency: 5.02 × 10¹4 Hz; Wavelength: 5.99 × 10^−7 m; Total energy in 1 mole: 178.2 kJ; Color: Yellow
b) Frequency: 5.99 × 10¹4 Hz; Wavelength: 5.02 × 10^−7 m; Total energy in 1 mole: 178.2 kJ; Color: Yellow
c) Frequency: 5.02 × 10¹4 Hz; Wavelength: 5.99 × 10^−7 m; Total energy in 1 mole: 124.6 kJ; Color: Green
d) Frequency: 5.99 × 10¹4 Hz; Wavelength: 5.02 × 10^−7 m; Total energy in 1 mole: 124.6 kJ; Color: Green

Answer 1

The frequency of the photon is 4.482 × 10^14 Hz and the wavelength is 6.68 × 10^-7 m. The total energy in 1 mole of these photons is 178.2 kJ. The color of the emitted light is yellow.

Step-by-step explanation:

To calculate the frequency of a photon, we can use the formula:

frequency = energy / Planck's constant

Given the energy of the photon is 2.961 × 10^-19 J, and Planck's constant is 6.626 × 10^-34 J·s, we can calculate the frequency:

frequency = (2.961 × 10^-19 J) / (6.626 × 10^-34 J·s) = 4.482 × 10^14 Hz

To calculate the wavelength, we can use the equation:

wavelength = speed of light / frequency

Given the speed of light is approximately 3.00 × 10^8 m/s:

wavelength = (3.00 × 10^8 m/s) / (4.482 × 10^14 Hz) = 6.68 × 10^-7 m

The total energy in 1 mole of these photons can be calculated by multiplying the energy of one photon by Avogadro's constant:

energy in 1 mole = (2.961 × 10^-19 J) * (6.022 × 10^23 mol^-1) = 178.2 kJ

The color of the emitted light depends on the wavelength. In this case, with a wavelength of 6.68 × 10^-7 m, the color of the emitted light would be yellow.