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प्रश्न
Use Bohr’s model of hydrogen atom to obtain the relationship between the angular momentum and the magnetic moment of the revolving electron.
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उत्तर
In the Bohr model of the hydrogen atom, the electron is modeled as a point negative charge rotating in a circular orbit about a fixed axis about a nucleus.
Let us consider,
r = radius of the orbit
v = velocity
e = charge of electron
m = mass of electron
Time period (T) = `"circumference"/"velocity"`
= `(2 pi r)/v`
Current (I) = `(-e)/T`
= `(-e)/((2 pi r)/v)`
= `(-e v)/(2 pi r)`
The magnetic moment due to a current loop enclosing an area A is given by:
ML = IA
= `(-e V)/(2 pi r) xx A`
= `(-e v)/(2 pi r) xx pi r^2`
= `(-e r v)/2`
= `(-m e r v)/(2 m)`
L = Angular momentum = mvr
So, ML = `(-e)/(2 m) L`
संबंधित प्रश्न
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The light emitted in the transition n = 3 to n = 2 in hydrogen is called Hα light. Find the maximum work function a metal can have so that Hα light can emit photoelectrons from it.
Why was a change in the Bohr Model of atom required? Due to which important development (s), concept of movement of an electron in an orbit was replaced by, the concept of probability of finding electron in an orbital? What is the name given to the changed model of atom?
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Who explained the hydrogen atom's spectrum using quantum ideas?
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