The threshold frequency $
u_0$ for a metal is $7.0 imes 10^{14}\ s^{-1}$. Calculate the kinetic energy of an electron emitted when radiation of frequency $
u = 1.0 imes 10^{15}\ s^{-1}$ hits the metal.

Question

The threshold frequency $
u_0$ for a metal is $7.0 	imes 10^{14}\ s^{-1}$. Calculate the kinetic energy of an electron emitted when radiation of frequency $
u = 1.0 	imes 10^{15}\ s^{-1}$ hits the metal.

Accepted Answer

> [!TLDR]
> The kinetic energy of the emitted electron is found using the photoelectric equation: $K = h(
u - 
u_0)$. Substituting the given frequencies and Planck’s constant gives $K = 1.99 	imes 10^{-19}\ 	ext{J}$.

The photoelectric effect is a beautiful example of light behaving as a particle. When a photon strikes a metal surface, it transfers its entire energy to an electron. But the electron needs a minimum energy just to escape the metal — that’s the work function, $\phi = h
u_0$. Any leftover energy becomes the electron’s kinetic energy.

So the core idea is simple: **photon energy in, work function out, kinetic energy left over.**

---

1. **Write down the photoelectric equation.**  
   Einstein’s photoelectric equation states:
   $$K = h
u - \phi$$
   where $K$ is the maximum kinetic energy of the emitted electron, $h$ is Planck’s constant, $
u$ is the frequency of incident radiation, and $\phi$ is the work function of the metal.

2. **Express the work function in terms of threshold frequency.**  
   The work function is the minimum energy needed to eject an electron, given by:
   $$\phi = h
u_0$$
   where $
u_0 = 7.0 	imes 10^{14}\ 	ext{s}^{-1}$ is the threshold frequency.

3. **Substitute into the equation.**  
   This gives:
   $$K = h
u - h
u_0 = h(
u - 
u_0)$$

4. **Plug in the numbers.**  
   Planck’s constant $h = 6.626 	imes 10^{-34}\ 	ext{J·s}$.  
   The incident frequency $
u = 1.0 	imes 10^{15}\ 	ext{s}^{-1}$.  
   So:
   $$
u - 
u_0 = (1.0 	imes 10^{15}) - (7.0 	imes 10^{14}) = 3.0 	imes 10^{14}\ 	ext{s}^{-1}$$

5. **Calculate the kinetic energy.**  
   $$K = (6.626 	imes 10^{-34}) 	imes (3.0 	imes 10^{14})$$
   $$K = 1.9878 	imes 10^{-19}\ 	ext{J}$$ …

Q.The threshold frequency $\nu_0$ for a metal is $7.0 \times 10^{14}\ s^{-1}$ . Calculate the kinetic energy of an electron emitted when radiation of frequency $\nu = 1.0 \times 10^{15}\ s^{-1}$ hits the metal.

Concept understanding — Photon Energy Calculation

Photon Energy Calculation

The Intuition First

The Precise Statement

Why Two Forms?

What This Tells You

A Worked Example

Common Mistake to Avoid …

Q.The threshold frequency ν0\nu_0ν0​ for a metal is 7.0×1014 s−17.0 \times 10^{14}\ s^{-1}7.0×1014 s−1. Calculate the kinetic energy of an electron emitted when radiation of frequency ν=1.0×1015 s−1\nu = 1.0 \times 10^{15}\ s^{-1}ν=1.0×1015 s−1 hits the metal.

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Q.The threshold frequency $\nu_0$ for a metal is $7.0 \times 10^{14}\ s^{-1}$ . Calculate the kinetic energy of an electron emitted when radiation of frequency $\nu = 1.0 \times 10^{15}\ s^{-1}$ hits the metal.

Unlock everything free for 14 days