Bohr Model Of The Hydrogen Atom

Step 1: Understanding orbital angular momentum.
The minimum orbital angular momentum of an electron in the hydrogen atom is given by the formula: where is the principal quantum number, and is the reduced Planck's constant, given by: For the minimum orbital angular momentum, the electron is in the ground state where . Thus, the minimum angular momentum is:
Step 2: Conclusion.
Therefore, the minimum orbital angular momentum is .

Step 1: Matter Waves and Their Characteristics.
Matter waves, described by de Broglie, are associated with particles and their wavelength is given by , where is Planck's constant and is the momentum. The wavelength does not depend on the charge of the particle but on its momentum.

Step 2: Conclusion.
Thus, the correct statement is that the wavelength of matter waves does not depend on the charge of the particle. Therefore, the correct answer is option .

According to Bohr's model, the energy of the electron in the -th orbit is given by:
We are given the energy . To find , we solve for in the equation:
Thus, the electron is in the second energy level ( ).
The angular momentum of the electron in the -th orbit is given by:
where is the reduced Planck’s constant.
For :
Thus, the angular momentum of the electron is: