The work function of lithium is 2.5 eV. what is the maximum wavelength of light that can cause the photoelectric effect in lithium?

Answer

To solve the question regarding the maximum wavelength of light that can cause the photoelectric effect in lithium, we will follow these steps:

### Step 1: Understand the Work Function
The work function (φ) is the minimum energy required to remove an electron from the surface of a material. For lithium, the work function is given as 2.5 eV.

### Step 2: Relate Work Function to Energy and Wavelength
The energy (E) of a photon can be expressed in terms of its frequency (ν) using the equation:
\[ E = hν \]
where \( h \) is Planck's constant. We can also relate frequency to wavelength (λ) using the equation:
\[ c = νλ \]
where \( c \) is the speed of light.

From these equations, we can derive that:
\[ E = \frac{hc}{λ} \]
Setting the energy equal to the work function gives us:
\[ φ = \frac{hc}{λ_{max}} \]

### Step 3: Rearrange the Equation to Find Maximum Wavelength
To find the maximum wavelength (λ_max) that can cause the photoelectric effect, we rearrange the equation:
\[ λ_{max} = \frac{hc}{φ} \]

### Step 4: Substitute Values
We know:
- Planck's constant \( h = 4.135667696 \times 10^{-15} \) eV·s (or approximately \( 1240 \) eV·nm when using \( c \) in nm/s)
- Speed of light \( c = 3 \times 10^8 \) m/s (or \( 1240 \) eV·nm)
- Work function \( φ = 2.5 \) eV

Now substituting these values into the equation:
\[ λ_{max} = \frac{1240 \text{ eV·nm}}{2.5 \text{ eV}} \]

### Step 5: Calculate the Maximum Wavelength
Calculating the above expression:
\[ λ_{max} = \frac{1240}{2.5} = 496 \text{ nm} \]

### Step 6: Convert to Angstroms (if needed)
To convert nanometers to angstroms (1 nm = 10 Å):
\[ λ_{max} = 496 \text{ nm} \times 10 = 4960 \text{ Å} \]

### Final Answer
The maximum wavelength of light that can cause the photoelectric effect in lithium is **496 nm** or **4960 Å**.

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