Modern Physics

Step 1: Using the de Broglie wavelength formula.
The de Broglie wavelength is given by: where: - (Planck's constant), - (mass of the object), - (velocity of the object).
Step 2: Substituting values into the formula.
Substitute the given values into the formula:
Step 3: Conclusion.
The de Broglie wavelength is , so the correct answer is (C).

Step 1: Understanding the scenario.
In trigonometry, the distance between the observer and the object can be related to the angle of elevation and the horizontal distance. The relationship between these quantities involves the cosine of half the angle in the context of angles involving .

Step 2: Applying the formula.
Given that the horizontal distance between the object and the observer is , the correct expression for the distance, based on standard trigonometric relationships, is:
Step 3: Conclusion.
The correct answer is (B) because it represents the proper trigonometric identity for the given angle and distance relation.

Step 1: Using the photon energy formula.
The energy of a photon is related to its frequency by the formula: where: - , - (Planck's constant), - is the frequency of the photon.
Step 2: Solving for frequency.
Rearrange the formula to solve for :
Step 3: Conclusion.
The frequency of the photon is , so the correct answer is (A).

Step 1: Using the energy-wavelength relation.
The energy of a photon is related to its wavelength by the equation: where: - , - , - , - is the wavelength.
Step 2: Solving for wavelength.
Rearranging the formula to solve for : Substitute the known values and solve.
Step 3: Conclusion.
The wavelength of the photon is , so the correct answer is (B).

Step 1: Using the energy formula for a photon.
The energy of a single photon can be calculated using Planck’s equation: where is the energy of the photon, is Planck's constant ( ), and is the frequency of the light.
Step 2: Substituting the values.
Given that the frequency , we can substitute the values into the formula:
Step 3: Conclusion.
The energy of each photon is , which corresponds to option (A).