Correct Answer  Option 3 : 2071 Å
Concept:
Photoelectric Effect:
 The phenomena by which rays of light falling on the metal surface make electrons ejected out of the metal surface is known as the Photoelectric Effect.

Work Function (ϕ) =The minimum energy required to eject an electron out of metal is known as work function.
 Threshold Frequency: The minimum frequency required so that the photoelectric effect can took place is called threshold frequency.
 It is given as
ϕ = h ν_{0}
where ν_{0} is the threshold frquency, the minimum frequency required for a light ray to eject an electron from that metal, h is Planck's constant.
This can also be written as
\(\phi = \frac{hc}{λ }\)
λ is the threshold wavelength or the maximum wavelength of the light so that the photoelectric effect can happen, c is the speed of light.
Calculation:
Given
Work function ϕ = 6 eV
Plancks constant h = 6.624 × 1034 Js
c = 3 × 108 m / sec
\(6 \times 1.602 × 10 ^{19} J= \frac{(6.624 × 10 ^{34})(3 × 10 ^8 )}{λ }\)
(1 ev = 1. 602 × 10 ^{19} J )
\(\implies λ = \frac{(6.624 × 10 ^{34})(3 × 10 ^8 )}{6 \times 1.602 × 10 ^{19} J }\)
λ ≈ 2071 Å
(1 Å = 10 ^{10} m )
So, the correct option is 2071 Å.
The Einstein equation for the photoelectric effect is given as:
K = hν  ϕ
Where h is Planck constant, ν is the frequency of light falling K is the kinetic energy of an electron ejected.
The light is said to be made up of small packets of energy each having energy equal to h ν, where ν is the frequency of the source light.
 The Equation can also be written as
K = hc/ λ  ϕ
c is the speed of light, c = 3 × 108 m/s, λ is the wavelength.