Question

Most of the light emitted by excited mercury atoms has wavelengths of 185, 254, 365, 436, 546 and 615nm. Which one of the following frequencies is emitted by mercury atoms?

a. 1.4 X 10^14s^-1
b. 4.1 X 10^14s^-1
c. 8.2 X 10^14s^-1
d. 8.2 X 10^15s^-1
e. 4.1 X 10^15s^-1

Answer 1

To determine which frequency matches the wavelengths given for mercury atoms, we use the relationship c = λν and calculate the frequency for each provided wavelength. The only frequency from the choices that corresponds to one of these wavelengths (365 nm) is 8.2 × 10¹⁴ s⁻¹. option C

Step-by-step explanation:

To find out which frequency is emitted by mercury atoms, we can use the formula for the speed of light (c) which relates wavelength (λ) and frequency (ν) by the equation c = λν. Since the speed of light is a constant (c = 3.00 × 108 m/s), we can rearrange the equation to solve for frequency: ν = c/λ.

Let’s solve for each wavelength given in the question:

For λ = 185 nm (which is 185 × 10-9 m), ν = 3.00 × 108 m/s ÷ 185 × 10-9 m ≈ 1.62 × 1015 s-1

For λ = 254 nm, ν ≈ 1.18 × 1015 s-1

For λ = 365 nm, ν ≈ 8.22 × 1014 s-1

For λ = 436 nm, ν ≈ 6.88 × 1014 s-1

For λ = 546 nm, ν ≈ 5.49 × 1014 s-1

For λ = 615 nm, ν ≈ 4.88 × 1014 s-1

The only frequency that matches an option given by the question is 8.22 × 1014 s-1, corresponding to the 365 nm wavelength, so the correct answer is c. 8.2 × 1014 s-1.