To determine the region of the incident radiation based on the given threshold frequency and stopping potential, we can analyze the information provided. The threshold frequency corresponds to the minimum energy required to eject an electron from the metallic surface, while the stopping potential indicates the maximum kinetic energy of the emitted electrons when they are subjected to an electric field.
Understanding the Concepts
The threshold frequency (\( \nu_0 \)) can be calculated using the equation:
E = h \cdot \nu_0
Where:
- E is the energy in electron volts (eV).
- h is Planck's constant, approximately \( 4.14 \times 10^{-15} \) eV·s.
- \( \nu_0 \) is the threshold frequency in hertz (Hz).
Given that the threshold energy is 6.2 eV, we can rearrange the formula to find the threshold frequency:
\( \nu_0 = \frac{E}{h} \)
Calculating the Threshold Frequency
Substituting the values:
\( \nu_0 = \frac{6.2 \text{ eV}}{4.14 \times 10^{-15} \text{ eV·s}} \approx 1.5 \times 10^{15} \text{ Hz} \)
This frequency is crucial because it indicates the minimum frequency of light required to eject electrons from the metal surface.
Analyzing the Stopping Potential
The stopping potential (V) relates to the maximum kinetic energy (KE) of the emitted electrons, which can be expressed as:
KE = eV
Where:
- e is the charge of an electron (approximately \( 1.6 \times 10^{-19} \) coulombs).
- V is the stopping potential in volts.
Given a stopping potential of 5V, the maximum kinetic energy of the emitted electrons is:
KE = 5 \text{ eV}
Determining the Energy of Incident Radiation
The energy of the incident radiation can be calculated as:
E_{incident} = KE + E_{threshold}
Substituting the values:
E_{incident} = 5 \text{ eV} + 6.2 \text{ eV} = 11.2 \text{ eV}
Identifying the Radiation Region
Now that we have the energy of the incident radiation (11.2 eV), we can categorize it into the appropriate electromagnetic spectrum region:
- X-ray region: Typically ranges from about 100 eV to several hundred keV.
- Ultraviolet region: Generally spans from about 3 eV to 100 eV.
- Infrared region: Usually falls between 0.001 eV to 1.7 eV.
- Visible region: Ranges from approximately 1.65 eV (red) to about 3.1 eV (violet).
Since 11.2 eV exceeds the upper limit of the ultraviolet region, it falls into the X-ray region of the electromagnetic spectrum.
Final Thoughts
In summary, the incident radiation that corresponds to a threshold frequency of 6.2 eV and a stopping potential of 5V is in the X-ray region. This analysis illustrates how energy levels and stopping potentials can help us classify different types of radiation based on their interactions with matter.
