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:

The longest wavelength is 2.19 × 10⁻⁷ m.

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,

$\nu = \frac{\phi }{h} =\frac{9.05 \times 10^{-19}J }{6.63 \times 10^{-34}J.s } =1.37 \times 10^{15}s^{-1}$

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,

$\lambda=\frac{c}{\nu } =\frac{3.00 \times 10^{8} m/s }{1.37 \times 10^{15} s^{-1} } =2.19 \times 10^{-7} m$

Answer 2

Answer: Option (A) is the correct answer.

Explanation:

The given data is as follows.

      Work function ($\phi$) = $9.05 \times 10^{19}$ J

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

                   $\phi = E = \frac{hc}{\lambda}$

where,   h = planck's constant = $6.63 \times 10^{-34}$ Js

              c = speed pf light = $3 \times 10^{8}$ m/s

           $\lambda$ = wavelength

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

                   $\phi = \frac{hc}{\lambda}$

        $9.05 \times 10^{19}$ J = $\frac{6.63 \times 10^{-34} Js \times 3 \times 10^{8}}{\lambda}$      

                    $\lambda$ = $\frac{19.89 \times 10^{-26}}{9.05 \times 10^{19}}$                

                                     = $2.197 \times 10^{7}$

Thus, we can conclude that long wavelength of light which will cause electrons to be emitted is $2.196 \times 10^{7}$.