Atom Structure Models

To solve the problem, we need to calculate how the energy of an electron in the first orbit of a Bohr hydrogen atom changes when the mass of the electron is doubled.

1. Energy of Electron in Bohr Model:
The energy of an electron in the -th orbit of a hydrogen atom is given by:

Where:
- is the ground state energy for hydrogen (with ),
- is the mass of the electron (can vary in hypothetical scenarios),
- is the actual mass of an electron,
- is the principal quantum number (for the first orbit, ).

2. Given Modification:
If the electron’s mass is doubled, then:

Final Answer:
The energy of the electron in the first orbit is .

To solve the problem, we need to extract the modulation index from the given equation of the amplitude modulated wave.

1. Given AM Wave Equation:

2. Standard AM Wave Equation:
The general form of an amplitude modulated signal is:

Where:
- is the carrier amplitude,
- is the modulation index,
- is the modulating frequency,
- is the carrier frequency.

3. Comparing with Standard Form:
From the given equation:
-
- The coefficient of is
Hence,

Final Answer:
The modulation index is 0.6.