Modern Physics

Step 1: Concept
According to Planck's equation, , where is energy and is frequency.
Step 2: Analysis
. The unit of energy is Joule ( ) and the unit of frequency is .
Step 3: Conclusion
Thus, the unit of is .
Final Answer: (B)

Step 1: Concept
The boiling point of a liquid increases with an increase in external pressure.
Step 2: Mechanism
Inside a pressure cooker, the steam is trapped, which significantly increases the internal pressure.
Step 3: Effect
This high pressure raises the boiling point of water above , allowing the food to cook at a higher temperature.
Step 4: Conclusion
The higher temperature speeds up the chemical and physical changes required for cooking.
Final Answer: (b)

Step 1: Energy change due to relativistic motion.
The total energy of a moving particle is given by: where is the Lorentz factor, is the velocity of the electron, and is the speed of light.

Step 2: Calculate the change in energy.
For an electron accelerated to , we calculate : The total energy is: Thus, the change in energy is:

Step 1: Use the kinetic energy formula for an accelerated electron.
The kinetic energy gained by the electron when it is accelerated through a potential difference is given by: where is the charge of the electron and .

Step 2: Calculate the velocity.
The kinetic energy is also related to the velocity by: Equating the two expressions for : Substituting , we can solve for :

Step 3: Conclusion.
The velocity acquired by the electron is , which is option (1).

Step 1: Understanding the Concept:
Work done .
Step 2: Detailed Explanation:
, .
.
Step 3: Final Answer:
Thus, work done = .

Step 1: Understanding the Concept:
De Morgan's theorem: .
Step 2: Detailed Explanation:
De Morgan's first law: Complement of product equals sum of complements.
Also, .
Step 3: Final Answer:
Thus, .

Step 1: Understanding the Concept:
Use Boltzmann distribution:
Step 2: Detailed Explanation:
Take wavelength at middle of visible range: . Energy difference: Thermal energy: Population ratio:
Step 3: Final Answer:

Step 1: Understanding the Concept:
Rydberg formula: .
Step 2: Detailed Explanation:
Balmer first line ( ):
Lyman first line ( ):

Step 3: Final Answer:
.

Step 1: Understanding the Concept:
Energy: , so .
Step 2: Detailed Explanation:
cm/s m/s

Step 3: Final Answer:
C/kg.

Step 1: Understanding the Concept:
The stopping potential is related to maximum KE: .
Step 2: Detailed Explanation:

Step 3: Final Answer:
Maximum KE of photoelectrons eV.

Step 1: Understanding the Concept:
LASER = Light Amplification by Stimulated Emission of Radiation.
Step 2: Detailed Explanation:
Laser operates in visible, UV, or IR region (light). MASER is for microwaves.
Step 3: Final Answer:
Ultraviolet or visible region.

Step 1: Understanding the Concept:
Convert to same trigonometric function.
Step 2: Detailed Explanation:

Also =
Phase difference =
Step 3: Final Answer:
Phase difference is .

Step 1: Understanding the Concept:
Water density maximum at 4°C.
Step 2: Detailed Explanation:
Using gas law incorrectly: gives 552°C, not in options.
Step 3: Final Answer:
None of these.