Consider bohr theory for hydrogen atom. The magnitude of angular momentum,orbital radius and velocity of the electron in n^th energy state in a hydrogen atom are l,r,v respectively.find out the value of 'x' if product of the time period of v,r,l (vrl) is directly proportional to n^x
Answers
Answer:
As the angular momentum(l) has magnitude l = m*v*r = nh/2π.
Where m is the mass of electron v is the velocity and r is the radius and n is the number of electrons.
Now, v^2 * r^2 * l^2 will be:
On putting the values, (n^2*h^2)/(4*π^2*m^2) * (n^2*h^2)/(4*π^2*) .
So, (n^4*h^4)/(16*π^4*m^4) in which the (h^4)/(16*π^4*m^4) will be constant hence the value of v^2 * r^2 * l^2 = n^4.
Or, (v*r*l) = n^2.
Since it is n^x hence the value of x will be 2.
Answer:As the angular momentum(l) has magnitude l = m*v*r = nh/2π.
Where m is the mass of electron v is the velocity and r is the radius and n is the number of electrons.
Now, v^2 * r^2 * l^2 will be:
On putting the values, (n^2*h^2)/(4*π^2*m^2) * (n^2*h^2)/(4*π^2*) .
So, (n^4*h^4)/(16*π^4*m^4) in which the (h^4)/(16*π^4*m^4) will be constant hence the value of v^2 * r^2 * l^2 = n^4.
Or, (v*r*l) = n^2.
Since it is n^x hence the value of x will be 2
Explanation: