Bohr S Model For Hydrogen Atom

Step 1: De Broglie wavelength of the electron The electron is in the orbit of a hydrogen-like atom with atomic number . In the Bohr model, the radius of the -th orbit is: For : where is the first Bohr radius of the hydrogen atom ( ). The velocity of the electron in the -th orbit is: For : Substitute : Momentum of the electron: De Broglie wavelength of the electron: Alternatively, using the Bohr quantization: Step 2: De Broglie wavelength of the neutron The neutron has thermal energy . Using kinetic energy: Momentum of the neutron: De Broglie wavelength: Step 3: Equate the de Broglie wavelengths Squaring both sides: Step 4: Use the given temperature expression Equating both expressions: Cancel and : Step 5: Substitute the Bohr radius Substitute into the earlier expression: Step 6: Verify with the alternative electron wavelength Using: Equating: Compare with: Final Answer: