Question

What is the number of photons of light with a wavelength of 4000 pm that provide 1 joule of energy?
it is from class 11

Answer 1

$\huge \mathfrak {Answer:-}$

 E = hν  (1)

 c = νλ

 E = hc / λ

The energy of 1 photon in a radiation of wavelength 400 nm is 

$= (6.63 \times 10^{ - 34} \times 3 \times 10 ^{8} ) \div (4 \times 10^{ - 7} )$

$= 4.972 \times 10 ^{ - 19} J$

Now,

The $\bold{number\:of\: photons}$ that would be required to provide an energy of 1 joule 

$=( \frac{1}{4.972 \times 10 ^{ - 19} } )$

$= 2.011 \times 10 ^{18}$

Therefore $2.011 \times 10 ^{18}$ of photons would be required to provide 1 Joule of energy. 

$\huge {Be\:Brainly}$❤️

Answer 2

2.012 * 10^16

Explanation:

Energy  of one photon (E) = hv

Energy of ‘n’ photons (En) = nhv => n = Enλ/hc

Where λ is the wavelength of the photons:

= 4000 pm = 4000 * 10^-12 meter

c denotes the speed of light in vacuum = 3 * 10^8 m/sec

h is plancks constant whose value = 6.26 * 10^-34 j/sec

Substituting these values in the expression for n:

n = 1 * 4000 * 10^-12 /( 6.26 * 10^-34)(3*10^5)

= 2.012 * 10^16

Hence, the number of photons with a wavelength of 4000 pm and energy of 1 J are 2.012 * 10^16.