Question 227: Dual Nature of Matter and Radiation

Question

The surface of a metal is illuminated with the light of $$400$$ $$nm.$$ The kinetic energy of the ejected photoelectrons was found to be $$1.68$$ $$eV.$$ The work function of the metal is : $$\left( {hc = 1240eV.nm} \right)$$

Accepted Answer

The photoelectric effect equation, which relates the energy of the incident light to the kinetic energy of the ejected photoelectrons and the work function of the metal, is given by:
$E = K_{\max} + W$,
where
$E$ is the energy of the incident light,
$K_{\max}$ is the maximum kinetic energy of the photoelectrons, and
$W$ is the work function of the metal.
The energy of the incident light can be calculated using the formula $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength of the light. However, given that $hc = 1240$ eVÃ¢ÂÂnm, we can simplify this to $E = \frac{1240}{\lambda}$.
Substituting the given values into this equation, we have:
$E = \frac{1240}{400} = 3.1$ eV.
We can then substitute these values into the photoelectric effect equation:
$3.1 	ext{ eV} = 1.68 	ext{ eV} + W$,
which simplifies to:
$W = 3.1 	ext{ eV} - 1.68 	ext{ eV} = 1.42$ eV.
Rounding to two decimal places, the work function of the metal is therefore approximately $1.42$ eV.
Thus, Option A: $1.41$ eV is the closest to the correct answer.

Answer

$$1.41$$ $$eV$$

Answer

$$1.51$$ $$eV$$

Answer

$$1.68$$ $$eV$$

Answer

$$3.09$$ $$eV$$

Dual Nature of Matter and Radiation

The surface of a metal is illuminated with the light of $400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is : \left( {hc = 1240eV.nm} \right)

Choose the correct answer: