Question

The speed of an electron in an orbit around hydrogen atom is 2.2*10^6 ms^-1.It takes 1.5*10^-16 s for the electron to complete one orbit. Calculate the radius of the orbit. please help me ASAP!!

Answer 1

The radius of the orbit is:
`R=0.525 \AA`

Explanation:

The period of a circular motion is the time to complete one orbit, then:

`T=1.5*10^(-16)s`

Now, let's recall the tangential speed can be written as:

`v=(2\pi R)/(T)`

R is the radius of the motion.

Let's solve the above equation for R.

`R=(vT)/(2 \pi)`

`R=(2.2*10^(6)1.5*10^(-16))/(2 \pi)`

`R=(2.2*10^(6)1.5*10^(-16))/(2 \pi)`

`R=5.25*10^(-11) \: m`

Therefore, the radius of the orbit is:
`R=0.525 \AA`

I hope it helps you!

Answer 2

5.3×10⁻¹¹ m

Explanation:

Applying,

v = 2πr/t................ Equation 1

Where v = speed of the electron in the orbit, r = radius of the orbit, t = time, π = pie

make r the subject of the equation

r = vt/2π................ Equation 2

From the question,

Given: v = 2.2×10⁶ m/s, t = 1.5×10⁻¹⁶ s

Constant: π = 3.14

Susbtitute these values into equation 2

r = (2.2×10⁶×1.5×10⁻¹⁶)/(3.14×2)

r = (3.3×10⁻¹⁰)/6.28

r = 5.3×10⁻¹¹ m

Hence the radius of the orbit is 5.3×10⁻¹¹ m