he minimum energy required to eject an electron from gadolinium is 4.65 x 10−19 J. Determine
if a photon of wavelength 575 nm can eject an electron from europium

To determine whether a photon of wavelength \( 575 \, \text{nm} \) can eject an electron from europium, we will compare the energy of this photon to the energy required to eject an electron from gadolinium, which is \( 4.65 \times 10^{-19} \, \text{J} \).

### Step 1: Calculate the energy of the photon

The energy of a photon \( E \) can be calculated using the formula:

\[
E = \frac{h \cdot c}{\lambda}
\]

where:
- \( h = 6.626 \times 10^{-34} \, \text{J·s} \) (Planck's constant),
- \( c = 3.00 \times 10^8 \, \text{m/s} \) (speed of light),
- \( \lambda = 575 \, \text{nm} = 575 \times 10^{-9} \, \text{m} \) (wavelength of the photon).

### Step 2: Plug in the values and solve for \( E \)

Now, let's calculate the energy of the photon.

\[
E = \frac{(6.626 \times 10^{-34}) \cdot (3.00 \times 10^8)}{575 \times 10^{-9}}
\]

I'll compute this value next.The energy of the photon with a wavelength of \( 575 \, \text{nm} \) is approximately \( 3.46 \times 10^{-19} \, \text{J} \).

### Step 3: Compare with the required energy
The minimum energy required to eject an electron from gadolinium is \( 4.65 \times 10^{-19} \, \text{J} \).

Since the photon energy \( 3.46 \times 10^{-19} \, \text{J} \) is less than the required \( 4.65 \times 10^{-19} \, \text{J} \), this photon does not have enough energy to eject an electron from europium.

### Conclusion:
A photon of wavelength \( 575 \, \text{nm} \) cannot eject an electron from europium if the energy requirement is similar to that of gadolinium.

---

Would you like more details on photon energy or have any other questions? Here are 5 related questions:

1. How is the energy of a photon affected by changes in wavelength?
2. What is the photoelectric effect and how does it relate to this problem?
3. What are the typical energy thresholds for ejecting electrons from different elements?
4. How does Planck's constant influence photon energy calculations?
5. Could a photon with a higher frequency eject an electron in this case?

**Tip**: Shorter wavelengths correspond to higher-energy photons because energy is inversely proportional to wavelength.

The minimum energy required to eject an electron from gadolinium is 4.65 x 10−19 J. Determine if a photon of wavelength 575 nm can eject an electron from europium.

Explore how to calculate the energy of a photon with a wavelength of 575 nm and compare it to the minimum energy required to eject an electron from gadolinium (4.65 x 10−19 J). Learn about photon energy, Planck's constant, and the photoelectric effect, suitable for Grades 11-12 physics students.

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