Question

) The wave length of light is 7000 A. The no. of photons required to provide 20J of energy is
approximately
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Answer 1

Question:

Wavelength of light 7000 A . Number of photons required to provide 20J energy.

Answer:

Photons required : $\rm\pink{ 7 \times 10^{19}}$

Given:

Wavelength of light : 7000 A.

Energy : 20 J.

To Find:

We are given ,

Wavelength of light (λ) : 7000 A.

Energy (E) : 20 J.

Let , the number of photons be n.

We know,

$e = nh \nu$

............. plank's energy equation.

Where ,

e = energy

n= number of photons

h= plank's constant

v = frequency

we know,

$h = 6.626 \times {10}^{ - 34} J$

$but \: \: \nu = \frac{c}{\lambda}$

$c = 3 \times {10}^{8} \frac{m}{s}$

also ,

$7000A = 7000 \times 1 {10}^{ - 10}$

$\rm\large{20 = n \times 6.626 \times {10}^{ - 34} \times \frac{3 \times {10}^{8} }{7000 \times {10}^{ - 10} }}$

$\rm\large{n = \frac{20 \times 7000 {10}^{ - 10} }{6.626 \times {10}^{34} \times 3 \times {10}^{8} }}$

$\rm\large{n = \frac{2 \times 7 \times {10}^{4} {10}^{ - 10} }{6.626 \times 3 \times {10}^{ - 26} }}$

$\rm\large{n = \frac{14 \times {10}^{6} }{6.626 \times 3 {10}^{ - 26} }}$

$\rm\large{n = \frac{14 \times {10}^{6} {10}^{26} }{6.626 \times 3}}$

$\rm\large{n = \frac{14 \times {10}^{20} }{6.626 \times 3} }$

$\rm\large{n = \frac{14 \times {10}^{20} }{19.878} }$

$\rm\large{n = 7.04 \times {10}^{19} }$

Number of photons : $\rm\large\pink{ 7 \times 10^{19} \ ...... ( approx )}$