Question

, Platinum, which s widely used as a catalyst, has a work function ф (the minimum ene needed to eject an electron from the metal surface) of 9.05 x 1019 J. What is the longe wavelength of light which will cause electrons to be emitted? A) 2.196 x 107 m B) 4.553 x 10-6 m C) 5.654 x 10 m Ans: A D) E) 1.370 x 1015 m >10 nm

Answer 1

Answer: Option (A) is the correct answer.

Step-by-step explanation:

The given data is as follows.

Work function (
`\phi`) =
`9.05 * 10^(19)` J

Now, relation between work function and wavelength is as follows.

`\phi = E = (hc)/(\lambda)`

where, h = planck's constant =
`6.63 * 10^(-34)` Js

c = speed pf light =
`3 * 10^(8)` m/s

`\lambda` = wavelength

As work function is also known as binding energy. Therefore, putting the given values into the above formula as follows.

`\phi = (hc)/(\lambda)`

`9.05 * 10^(19)` J =
`(6.63 * 10^(-34) Js * 3 * 10^(8))/(\lambda)`

`\lambda` =
`(19.89 * 10^(-26))/(9.05 * 10^(19))`

=
`2.197 * 10^(7)`

Thus, we can conclude that long wavelength of light which will cause electrons to be emitted is
`2.196 * 10^(7)`.

Answer 2

The longest wavelength is 2.19 × 10⁻⁷ m.

Step-by-step explanation:

The work function (ф) is the minimum energy required to remove an electron from the surface of a metal. The minimum frequency required in a radiation to submit such energy can be calculated with the following expression.

ф = h × ν

where,

h is the Planck's constant (6.63 × 10⁻³⁴ J.s)

ν is the threshold frequency for the metal

In this case,

`\\u = (\phi )/(h) =(9.05 * 10^(-19)J  )/(6.63 * 10^(-34)J.s ) =1.37 * 10^(15)s^(-1)`

We can find the wavelength associated to this frequency using the following expression.

c = λ × ν

where,

c is the speed of light (3.00 × 10⁸ m/s)

λ is the wavelength

Then,

`\lambda=(c)/(\\u ) =(3.00 * 10^(8) m/s  )/(1.37 * 10^(15) s^(-1) ) =2.19 * 10^(-7) m`