In a hydrogen atom, the radius of nth Bohr orbit is rn. The graph between log(rn/r1) and logn will be

Question

In a hydrogen atom, the radius of nth Bohr orbit is rn. The graph between log(rn/r1) and logn will be (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

We know that rn propto n2 or (rn/r1) = n2 So, log(rn /r1) = 2 log n Hence, the graph between log(rn /r1) and log n will be a straight line passing through origin. The positive slope is given by tan θ = 2.

Q. In a hydrogen atom, the radius of $n^{t h}$ Bohr orbit is $r_{n}$ . The graph between $l o g (r_{n} / r_{1})$ and $l o g n$ will be

We know that $r_{n} \propto n^{2}$ or $(r_{n} / r_{1}) = n_{2}$
So, $l o g (r_{n} / r_{1}) = 2 l o g n$
Hence, the graph between $l o g (r_{n} / r_{1})$ and $l o g n$ will be a straight line passing through origin.
The positive slope is given by $t an θ = 2$ .

Q. In a hydrogen atom, the radius of nth Bohr orbit is rn​. The graph between log(rn​/r1​) and logn will be

We know that rn​∝n2 or (rn​/r1​)=n2​ So, log(rn​/r1​)=2logn Hence, the graph between log(rn​/r1​) and logn will be a straight line passing through origin. The positive slope is given by tanθ=2.

Q. In a hydrogen atom, the radius of $n^{t h}$ Bohr orbit is $r_{n}$ . The graph between $l o g (r_{n} / r_{1})$ and $l o g n$ will be

We know that $r_{n} \propto n^{2}$ or $(r_{n} / r_{1}) = n_{2}$
So, $l o g (r_{n} / r_{1}) = 2 l o g n$
Hence, the graph between $l o g (r_{n} / r_{1})$ and $l o g n$ will be a straight line passing through origin.
The positive slope is given by $t an θ = 2$ .