The number of photons emitted by a monochromatic (single frequency) infrared range finder of power 1 mW and wavelength of 1000 nm, in 0.1 second is x $$\times$$ 1013. The value of x is _____________. (Nearest integer)
$$\Rightarrow$$ n = 5.02 $$\times$$ 1014 = 50.2 $$\times$$ 1013
$$\Rightarrow$$ 50 (nearest integer)
2
JEE Main 2021 (Online) 27th August Morning Shift
Numerical
The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is equal to $${{{h^2}} \over {xma_0^2}}$$. The value of 10x is ___________. (a0 is radius of Bohr's orbit) (Nearest integer) [Given : $$\pi$$ = 3.14]
A metal surface is exposed to 500 nm radiation. The threshold frequency of the metal for photoelectric current is 4.3 $$\times$$ 1014 Hz. The velocity of ejected electron is ____________ $$\times$$ 105 ms$$-$$1 (Nearest integer)
[Use : h = 6.63 $$\times$$ 10$$-$$34 Js, me = 9.0 $$\times$$ 10$$-$$31 kg]
Your Input ________
Answer
Correct Answer is 5
Explanation
$$\upsilon $$ : speed of electron having max. K.E.
$$\Rightarrow$$ from Einstein equation : E = $$\phi$$ + K.E.max
An accelerated electron has a speed of 5 $$\times$$ 106 ms$$-$$1 with an uncertainty of 0.02%. The uncertainty in finding its location while in motion is x $$\times$$ 10$$-$$9 m. The value of x is ____________. (Nearest integer)
[Use mass of electron = 9.1 $$\times$$ 10$$-$$31 kg, h =6.63 $$\times$$ 10$$-$$34 Js, $$\pi$$ = 3.14]
Your Input ________
Answer
Correct Answer is 58
Explanation
$$\Delta v = {{0.02} \over {100}} \times 5 \times {10^6} = {10^3}$$ m/s