Question

Assume that the radius of the first Bohr orbit of hydrogen atom is $0.6Å$. The radius of the third Bohr orbit of $He^+$is _______ picometer. (Nearest Integer)

Answer 1

Correct Answer: 270

To solve this problem, we will use the formula for the radius of the n^th Bohr orbit, which is given by:
r_n = r₁ × n²/Z,
where r_n is the radius of the n^th orbit, r₁ is the radius of the first orbit, n is the orbit number, and Z is the atomic number.

For hydrogen, the atomic number Z is 1. Given the first Bohr orbit radius for hydrogen is 0.6 Å, this becomes the reference for calculations for other elements like He⁺, where Z = 2.

First, convert the radius of the first orbit from Ångström to picometers:
1 Å = 100 pm, therefore 0.6 Å = 60 pm.

Now, calculate the radius of the third Bohr orbit for He⁺:
r₃ = 60 pm × (3)²/2 = 60 pm × 9/2 = 270 pm.

Finally, verify the value:
The calculated radius is 270 pm, which falls within the expected range of 270 to 270 pm as specified.

The radius of the third Bohr orbit of He⁺ is 270 pm, confirming the computed value is accurate.