Dual Nature Of Radiation And Matter

The stopping potential in the photoelectric effect is determined by the energy of the photons and the work function of the metal, not by the intensity or distance of the light source. According to the photoelectric effect, electrons are ejected when photons with energy greater than the work function hit the metal surface. The stopping potential is given by the equation:

where:

• is Planck's constant.
• is the frequency of the incident light.
• is the work function of the metal.
• is the charge of an electron.

The stopping potential depends only on the frequency of the incident light and is independent of the intensity or the distance of the light source from the metal surface. As such, removing the source farther from the emitting metal does not affect the frequency of the light, and thus, the stopping potential will remain constant.
Therefore, the correct answer is: Will remain constant

To calculate the de Broglie wavelength of an electron accelerated through a potential difference of 100 V, we'll follow these steps:

1. Given Data:
- Potential difference (V) = 100 V
- Charge of electron (e) = 1.602 × 10^-19 C
- Mass of electron (m) = 9.109 × 10^-31 kg
- Planck's constant (h) = 6.626 × 10^-34 J·s

2. Calculate the Kinetic Energy:
The kinetic energy gained by the electron is:
KE = eV = (1.602 × 10^-19 C)(100 V) = 1.602 × 10^-17 J

3. Determine the Electron's Velocity:
Using KE = ½mv²:
v = √(2KE/m) = √(2 × 1.602 × 10^-17 J / 9.109 × 10^-31 kg)
≈ 5.93 × 10⁶ m/s

4. Calculate the de Broglie Wavelength:
Using λ = h/p = h/(mv):
λ = (6.626 × 10^-34 J·s) / (9.109 × 10^-31 kg × 5.93 × 10⁶ m/s)
≈ 1.23 × 10^-10 m = 1.23 Å

5. Simplified Formula (Alternative Approach):
For electrons, we can use the shortcut formula:
λ = h/√(2meV)
= 6.626 × 10^-34/√(2 × 9.109 × 10^-31 × 1.602 × 10^-19 × 100)
= 1.23 × 10^-10 m

6. Interpretation:
This wavelength (1.23 Å) is comparable to atomic spacing in crystals, which is why electron beams are useful for studying crystal structures.

Final Answer:
The de Broglie wavelength of an electron accelerated through 100 V is 1.23 × 10^-10 m (or 1.23 Å).

We need to determine the general effect of increasing temperature on the electron work function of a metal.

1. Understanding the Work Function:
The work function of a metal is the minimum energy required to remove an electron from its surface to infinity. It is a material-specific property, typically denoted by , and depends on the electronic structure of the metal.

2. Temperature Dependence:
The work function is primarily determined by the metal's surface properties and its Fermi energy level, which are intrinsic characteristics. However, temperature can influence the work function indirectly:
- As temperature increases, thermal energy causes lattice vibrations (phonons) and can slightly alter the electronic energy levels and surface conditions.
- These effects may lead to a small decrease in the work function because thermal energy can assist in overcoming the potential barrier, effectively reducing the energy needed to eject an electron.
- Experimental studies show that for most metals, the work function decreases slightly with increasing temperature, often on the order of a few meV per 100 K, due to thermal expansion and changes in the surface dipole layer.

3. General Trend:
While the effect is small and varies by metal, the general trend is that the work function decreases as temperature increases, as thermal effects facilitate electron emission (e.g., in thermionic emission).

Final Answer:
In general, as the temperature increases, the electron work function of a metal would decrease.

We need to determine the height of a geostationary satellite above Earth's surface, given the correct answer is approximately 36,000 km.

1. Geostationary Orbit Characteristics:
A geostationary satellite orbits Earth in the equatorial plane with an orbital period equal to Earth's rotation period, approximately 24 hours (86,400 seconds). This ensures the satellite remains fixed relative to a point on Earth's surface.

2. Orbital Dynamics:
For a circular orbit, the centripetal force required for the satellite's motion is provided by Earth's gravitational force:


where is the satellite's mass, is the orbital velocity, is the distance from Earth's center, is the gravitational constant, and is Earth's mass. Simplifying:


The orbital velocity is also related to the period :


Equating:

3. Solving for Orbital Radius:
Square both sides:


Rearrange:


Using , , , and :

4. Calculating Height:
The height is the altitude above Earth's surface, so subtract Earth's mean radius ( ):


This value is often rounded to approximately 36,000 km in standard references due to slight variations in constants (e.g., or refined ) or simplified calculations.

Final Answer:
The height of a geostationary satellite is approximately .