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Question: An important spectral emission line has a wavelength of 21 cm. The corresponding photon energy is....

An important spectral emission line has a wavelength of 21 cm. The corresponding photon energy is.

A

5.9×10−4eV5.9 \times 10 ^ { - 4 } \mathrm { eV }

B

5.9×10−6eV5.9 \times 10 ^ { - 6 } \mathrm { eV }

C

5.9×10−8eV5.9 \times 10 ^ { - 8 } \mathrm { eV }

D

11.8×10−6eV11.8 \times 10 ^ { - 6 } \mathrm { eV }

(h=6.62×10−34 J;c=3×108 m/s)\left( h = 6.62 \times 10 ^ { - 34 } \mathrm {~J} ; c = 3 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)

Answer

5.9×10−6eV5.9 \times 10 ^ { - 6 } \mathrm { eV }

Explanation

Solution

E=hcλ=3×108×6.62×10−340.21×1.6×10−19=5.9×10−6eVE = \frac { h c } { \lambda } = \frac { 3 \times 10 ^ { 8 } \times 6.62 \times 10 ^ { - 34 } } { 0.21 \times 1.6 \times 10 ^ { - 19 } } = 5.9 \times 10 ^ { - 6 } \mathrm { eV }