Question

6. Calculate the number of photons having a wavelength of 10.0 m required to produce 1.0 kJ of energy

Answer 1

We have to calculate the number of photons having a wavelength of 10μm required to produced 1 kJ of energy.

we know, “Energy of each photon is inversely proportional to wavelength”. and energy of photon is given by, E = hc/λ ,

where h is plank's constant, c is the speed of light and λ is wavelength.

here, wavelength , λ = 10μm = 10¯⁵ m

speed of light in vacuum, c = 3 × 10^8 m/s

plank's constant , h = 6.63 × 10¯³⁴ J.s

let number of photons = n

⇒Total energy = n × energy of each photon

⇒1 kJ = n × (6.63 × 10¯³⁴ × 3 × 10^8)/(10¯⁵)

⇒10³ = n × 19.89 × 10¯²¹

⇒n = 1/19.89 × 10²⁴ ≈ 5 × 10²²

Therefore the number of photons required to produced 1 kJ energy is 5 × 10²².

Answer 2

Given:

Wavelength of the photons (λ)= 10×10⁻⁶m

Total energy = 10³ J

To find:

Number of photons that produce the given amount of energy.

Explanation:

Step 1

• We have been given the total energy produced by n number of photons.

       That is,

      Total energy of photons = number of photons × energy of each photon.

• We know, energy of photon is given by Planck's equation, that is,

                                            E = hν

                        where h = 6.63×10⁻³⁴ (Planck's constant)

• From the relation, c = νλ ,

                                 E = h c/λ

Substituting the values, we get

$E = \frac{6.63 * 10^{-34} * 3*10^{8} }{10*10^{-6} } \\E = 19.89 * 10^{-21}$

Step 2

We have the total energy = 10³ J

Therefore,

Number of electrons,

$n=\frac{10^{3} }{19.89*10^{-21} }$

n = 0.05 × 10²⁴

or

n = 5×10²²

Final answer:

Hence, the number of electrons required to produce 1 KJ of energy is 5×10²².