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Structure of Atom question

2021 · 1 Sep · Shift 2 · Q20
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Structure of Atom question

2021 · 1 Sep · Shift 2 · Q20

JEE MainChemistryStructure of AtomNumerical+4 / −1
A 50 watt bulb emits monochromatic red light of wavelength of 795 nm. The number of photons emitted per second by the bulb is x ×\times× 1020. The value of x is ‾\underline{\hspace{2cm}}​. [Given : h = 6.63 ×\times× 10 −-− 34 Js and c = 3.0 ×\times× 108 ms −-− 1]
Numerical answer
View written solutionFree

Correct answer: 2

  1. Given data
  • Power of bulb: P=50 W=50 J s−1P = 50\,\text{W} = 50\,\text{J s}^{-1}P=50W=50J s−1
  • Wavelength of light: λ=795 nm=795×10−9 m\lambda = 795\,\text{nm} = 795 \times 10^{-9}\,\text{m}λ=795nm=795×10−9m
  • Planck's constant: h=6.63×10−34 J sh = 6.63 \times 10^{-34}\,\text{J s}h=6.63×10−34J s
  • Speed of light: c=3.0×108 m s−1c = 3.0 \times 10^8\,\text{m s}^{-1}c=3.0×108m s−1
  1. Energy of one photon

Using, E=hcλE = \frac{hc}{\lambda}E=λhc​

Substitute the values: E=(6.63×10−34)(3.0×108)795×10−9E = \frac{(6.63 \times 10^{-34})(3.0 \times 10^8)}{795 \times 10^{-9}}E=795×10−9(6.63×10−34)(3.0×108)​

First calculate the numerator: 6.63×3.0=19.896.63 \times 3.0 = 19.896.63×3.0=19.89 So, hc=19.89×10−26=1.989×10−25 J mhc = 19.89 \times 10^{-26} = 1.989 \times 10^{-25}\,\text{J m}hc=19.89×10−26=1.989×10−25J m

Now, E=1.989×10−25795×10−9E = \frac{1.989 \times 10^{-25}}{795 \times 10^{-9}}E=795×10−91.989×10−25​

Since 795×10−9=7.95×10−7795 \times 10^{-9} = 7.95 \times 10^{-7}795×10−9=7.95×10−7, E=1.989×10−257.95×10−7E = \frac{1.989 \times 10^{-25}}{7.95 \times 10^{-7}}E=7.95×10−71.989×10−25​

E≈0.25×10−18=2.5×10−19 JE \approx 0.25 \times 10^{-18} = 2.5 \times 10^{-19}\,\text{J}E≈0.25×10−18=2.5×10−19J

  1. Number of photons emitted per second

Power is energy emitted per second, so N=PEN = \frac{P}{E}N=EP​

N=502.5×10−19N = \frac{50}{2.5 \times 10^{-19}}N=2.5×10−1950​

N=20×1019=2×1020N = 20 \times 10^{19} = 2 \times 10^{20}N=20×1019=2×1020

  1. Compare with the given form

We need N=x×1020N = x \times 10^{20}N=x×1020

So, x=2x = 2x=2

  1. Comparison with stored answer

Stored correct answer = 222

My derived answer also gives 222, so they agree.

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