The energy of a photo having a wavelength of 10-10m is (h= 6.63 x 10 -34Js, c =3.0 x 10 8$ms^{-1}$)

Analyze the question: We need the energy of a photon with wavelength λ = 10⁻¹⁰ m, given h = 6.63 × 10⁻³⁴ Js and c = 3.0 × 10⁸ m/s.

Concept: A photon's energy is related to its frequency and wavelength by:

E = hf, and since c = fλ, we get

E = hc / λ

Solution:

E = (6.63 × 10⁻³⁴ × 3.0 × 10⁸) / (10⁻¹⁰)

Numerator: 6.63 × 3.0 = 19.89, so hc = 19.89 × 10⁻²⁶ = 1.989 × 10⁻²⁵ J·m

Divide by 10⁻¹⁰:

E = 1.989 × 10⁻²⁵ ÷ 10⁻¹⁰ = 1.989 × 10⁻¹⁵ J ≈ 2.0 × 10⁻¹⁵ J

Check against the options:

• A. 2.0 × 10⁻¹⁵ J ✔ matches
• B, C, D are too large by factors of about 100 to 1000.

Tip: Remember hc ≈ 2 × 10⁻²⁵ J·m. For any wavelength, just divide 2 × 10⁻²⁵ by λ. Here, 2 × 10⁻²⁵ ÷ 10⁻¹⁰ = 2 × 10⁻¹⁵ J, which gives the answer quickly. Be careful with the exponent subtraction: −25 − (−10) = −15.