Answer:
486 nm
Step-by-step explanation:
From the question given above, the following data were obtained:
Energy (E) = 4.09×10¯¹⁹ J
Wavelength (λ) =?
Next, we shall determine the frequency of the photon. This can be obtained as follow:
Energy (E) = 4.09×10¯¹⁹ J
Planck's constant (h) = 6.63×10¯³⁴ Js
Frequency (f) =?
E = hf
4.09×10¯¹⁹ = 6.63×10¯³⁴ × f
Divide both side by 6.63×10¯³⁴
f = 4.09×10¯¹⁹ / 6.63×10¯³⁴
f = 6.17×10¹⁴ Hz
Next, we shall determine the wavelength of the photon. This can be obtained as follow:
Frequency (f) = 6.17×10¹⁴ Hz
Velocity of photon (v) = 3×10⁸ m/s
Wavelength (λ) =?
v = λf
3×10⁸ = λ × 6.17×10¹⁴
Divide both side by 6.17×10¹⁴
λ = 3×10⁸ / 6.17×10¹⁴
λ = 4.86×10¯⁷ m
Finally, we shall convert 4.86×10¯⁷ m to nm. This can be obtained as follow:
1 m = 1×10⁹ nm
Therefore,
4.86×10¯⁷ m = 4.86×10¯⁷ m × 1×10⁹ nm / 1 m
4.86×10¯⁷ m = 486 nm
Therefore, the wavelength of the photon is 486 nm