To tackle this problem, we need to analyze the information given about the metals A and B, their work functions, and the kinetic energies of the emitted electrons. Let's break down the details step by step.
Understanding the Concepts
When photons strike a metal surface, they can eject electrons if the energy of the photons exceeds the work function of the metal. The work function (φ) is the minimum energy required to remove an electron from the surface of the metal. The kinetic energy (K.E.) of the emitted electrons can be calculated using the equation:
K.E. = E_photon - φ
Where E_photon is the energy of the incoming photon.
Given Data
- Energy of photon striking metal A: 4.25 eV
- Maximum kinetic energy of electrons from metal A: Ta
- Energy of photon striking metal B: 4.20 eV
- Maximum kinetic energy of electrons from metal B: Tb = Ta - 1.50 eV
- De Broglie wavelength of electrons from metal B: λB = 2 * λA
Calculating the Work Functions
Let's denote the work functions of metals A and B as φA and φB, respectively. From the information provided, we can express the kinetic energies in terms of the work functions:
For metal A:
K.E. = Ta = E_photon - φA
Thus, we have:
Ta = 4.25 eV - φA
For metal B:
K.E. = Tb = E_photon - φB
Thus, we have:
Tb = 4.20 eV - φB
Relating Ta and Tb
From the problem, we know that:
Tb = Ta - 1.50 eV
Substituting the expressions for Ta and Tb, we get:
4.20 eV - φB = (4.25 eV - φA) - 1.50 eV
Rearranging gives:
φB = φA + 1.50 eV - 4.25 eV + 4.20 eV
φB = φA + 1.45 eV
Finding the Work Functions
Now, we can analyze the options provided:
- A: Work function of A is 2.25 eV
- B: Work function of B is 3.70 eV
- C: Ta = 2 eV
- D: Tb = 2.75 eV
If we assume φA = 2.25 eV, we can calculate φB:
φB = 2.25 eV + 1.45 eV = 3.70 eV
This means options A and B are consistent with each other.
Next, we calculate Ta:
Ta = 4.25 eV - φA = 4.25 eV - 2.25 eV = 2.00 eV
This confirms option C is also correct.
Now, we can find Tb:
Tb = Ta - 1.50 eV = 2.00 eV - 1.50 eV = 0.50 eV
This indicates that option D (Tb = 2.75 eV) is incorrect.
Final Thoughts
In summary, the incorrect statement among the options provided is D: Tb = 2.75 eV. The calculations show that the actual value of Tb is 0.50 eV, which does not match the given option. This exercise illustrates the importance of understanding the relationships between photon energy, work function, and kinetic energy in the photoelectric effect.
