Question

If the red line in the Balmer series has a wavelength of 656 nm, which of the following is closest to its frequency?

a. 4.6 × 10¹⁴ Hz
b. 4.6 × 10¹⁴ Hz
c. 2.1 × 10¹⁵ Hz
d. 2.1 × 10¹⁵ Hz

Answer 1

The frequency of the red line in the Balmer series with a wavelength of 656 nm is approximately so the closest given option is (a)
`4.6 × 10⁾¹⁴ Hz`.

Step-by-step explanation:

If the red line in the Balmer series has a wavelength of
`656 nm`, we can determine its frequency using the equation
`c = λf`,

where c is the speed of light (approximately
`3.00 × 108 m/s`),
`λ` is the wavelength, and f is the frequency.

First, we must convert the wavelength from nanometers to meters by multiplying by
`10-9`,

resulting in
`656 nm × 10-9 = 6.56 × 10-7 m`.

Next, we divide the speed of light by the wavelength to find the frequency:

`f = c / λ = (3.00 × 108 m/s) / (6.56 × 10-7 m) ≈ 4.57 × 1014 Hz`.

Therefore, the closest answer to the frequency of the red line in the Balmer series would be (a)
`4.6 × 1014 Hz`.