Question

Wavelength Of Light 7000A.No Of Photons Required To Provide 20J Energy

Answer 1

Answer:

$\large \text{7\times10^{19} }}$

Explanation:

Given :

Energy ( E )  = 20 J

Wavelength ( λ ) = 7000 A

We have to find numbers of photons.

Let numbers of photons be n.

We have planck's energy equation

$\large e=nhv$

where   e = energy

n  = numbers of photons

h = planck's constant

v = frequency

$\large \text{We know value of h =6.626\times10^{-34} \ J \ sec }\\\\\\\large \text{We also know that v is nothing but \dfrac{c}{\lambda} }\\\\\\\large \text{Value of c =3\times10^{8} \ m/sec }\\\\\\\large \text{Here wave length is in Agrotron }\\\\\\\large \text{convert it into metre ( m ) we get 7000\times10^{-10} \ m }}$

Now put the values in equation

$\large \text{ 20=n\times 6.626\times10^{-34} \times\dfrac{3\times10^{8}}{7000\times10^{-10}} }\\\\\\\large \text{ n=\dfrac{20\times7000\times10^{-10}}{6.626\times10^{-34}\times3\times10^{8}} }\\\\\\\large \text{ n=\dfrac{2\times7\times10^{4}\times10^{-10}}{6.626\times10^{-34}\times3\times10^{8}} }\\\\\\\large \text{ n=\dfrac{14\times10^{-6}}{6.626\times3\times10^{-26}} }\\\\\\\large \text{ n=\dfrac{14\times10^{-6}\times10^{26}}{6.626\times3} }$

$\large \text{ n=\dfrac{14\times10^{20}}{6.626\times3} }\\\\\\\large \text{ n=\dfrac{14\times10^{20}}{19.878} }\\\\\\\large \text{ n=\dfrac{140\times10^{19}}{19.878} }\\\\\\\large n=7.04\times10^{19}\\\\\\\large \text{About n=7\times10^{19} }$

Thus the numbers of photons is 7 × 10¹⁹.

Answer 2

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