Question

Calculate the energy in joule corresponding to light of wavelength 45 nm:
(Planck’s constant h = 6.63 × 10^-34 Js; speed of light c = 3 × 10⁸ ms^-1)

• A. 6.67 × 10¹¹
• B. 4.42 × 10^-15
• C. 4.42 × 10^-18
• D. 6.67 × 10¹⁵

Answer 1

The Correct Option is C

 To calculate the energy corresponding to a wavelength of light, we use the formula for energy of a photon:

\(E = \frac{h \cdot c}{\lambda}\)

where:

• \(E\) is the energy of the photon in joules (J).
• \(h = 6.63 \times 10^{-34}\) Js is Planck's constant.
• \(c = 3 \times 10^8\) m/s is the speed of light.
• \(\lambda = 45\) nm = \(45 \times 10^{-9}\) m is the wavelength of the light.

Substituting the given values into the formula:

\(E = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{45 \times 10^{-9}}\)

First, calculate the numerator:

\(6.63 \times 10^{-34} \times 3 \times 10^8 = 1.989 \times 10^{-25}\)

Then, calculate the denominator:

\(45 \times 10^{-9} = 4.5 \times 10^{-8}\)

Now, divide the numerator by the denominator to find the energy:

\(E = \frac{1.989 \times 10^{-25}}{4.5 \times 10^{-8}} = 4.42 \times 10^{-18}\) J

Thus, the energy corresponding to light of wavelength 45 nm is \(4.42 \times 10^{-18}\) J.

The correct answer is

4.42 × 10^-18

.