A stellar object is emitting radiation at 3.55 mm. If a detector is capturing 3.2×108 photons per second at this wavelength, what is the total energy of the photons detected in 1.0 hour?

E = 6.45 x 10⁻¹¹ J

Explanation:

First we need to find total number of photons detected in 1 hour. Therefore,

No. of Photons = n = (3.2 x 10⁸ photons/s)(1 h)(3600 s/1 h)

n = 11.52 x 10¹¹ photons

Now, the energy of these photons can be given by the formula:

E = nhc/λ

where,

E = Total Energy of the Photons = ?

h = Plank's Constant = 6.626 x 10⁻³⁴ J.s

c = speed of light = 3 x 10⁸ m/s

λ = wavelength of radiation = 3.55 mm = 3.55 x 10⁻³ m

Therefore,

E = (11.52 x 10¹¹)(6.626 x 10⁻³⁴ J.s)(3 x 10⁸ m/s)/(3.55 x 10⁻³ m)

E = 6.45 x 10⁻¹¹ J