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Show that the radius of the orbit in hydrogen atom varies as n2, where n is the principal quantum number of the atom. |
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Answer» Solution :de Broglie wavelength `lambda = (h)/(P)=(h)/(sqrt(2mqV))` Where, m = mass of charge particle, q = charge of particle, V = POTENTIAL DIFFERENCE (i)`lambda_(2)=(h^(2))/(sqrt(2mqV))` `V=(h^(2))/(sqrt(2mq lambda^(2)))` `THEREFORE (V_(P))/(V_(alpha))=(2m_(alpha)q_(alpha))/(2m_(p)q_(p))=(2xx4m2q)/(2mq)=(8)/(1)` `therefore V_(P) : V_(alpha)=8:1` (ii)`lambda = (h)/(mu), lambda_(P)=(h)/(m_(P)u_(P), lambda_(alpha))=(h)/(m_(alpha)V_(alpha))` `lambda_(P)=lambda_(alpha)` `(h)/(m_(P)u_(P))=(h)/(m_(alpha)u_(alpha))` `(u_(P))/(u_(alpha))=(m_(alpha))/(m_(P))=(4)/(1)=4:1` |
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