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What’s the radius of 1st orbit of He+ atom?
- a)0.1058 nm
- b)0.2156 nm
- c)0.00529 nm
- d)0.02645 nm
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
What’s the radius of 1storbit of He+atom?a)0.1058 nmb)0.2156 nmc...
The atomic radius of an atom is given by the formula rn = 52.9n2/Z pm, where rn is the radius of nth orbit of an atom and Z is the atomic number of that atom. For He+, n = 1 and Z =2. Radius = 52.9(1)/2 pm = 0.02645 nm.
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What’s the radius of 1storbit of He+atom?a)0.1058 nmb)0.2156 nmc...
Calculation of Radius of 1st Orbit of He+ Atom:
To determine the radius of the first orbit of a He+ atom, we can use the Bohr radius formula:
Bohr Radius (r) = n^2 h^2 / 4π^2 m e^2
Where:
- n = principal quantum number (for the first orbit, n = 1)
- h = Planck's constant (6.626 x 10^-34 m^2 kg / s)
- m = reduced mass of the electron and nucleus (2.4 x 10^-26 kg)
- e = elementary charge (1.6 x 10^-19 C)
Plugging in the values:
- n = 1
- h = 6.626 x 10^-34
- m = 2.4 x 10^-26
- e = 1.6 x 10^-19
Calculating the radius:
r = (1^2 x (6.626 x 10^-34)^2) / (4 x π^2 x 2.4 x 10^-26 x (1.6 x 10^-19)^2)
r = 0.02645 nm
Therefore, the radius of the first orbit of a He+ atom is 0.02645 nm, which corresponds to option D.
To determine the radius of the first orbit of a He+ atom, we can use the Bohr radius formula:
Bohr Radius (r) = n^2 h^2 / 4π^2 m e^2
Where:
- n = principal quantum number (for the first orbit, n = 1)
- h = Planck's constant (6.626 x 10^-34 m^2 kg / s)
- m = reduced mass of the electron and nucleus (2.4 x 10^-26 kg)
- e = elementary charge (1.6 x 10^-19 C)
Plugging in the values:
- n = 1
- h = 6.626 x 10^-34
- m = 2.4 x 10^-26
- e = 1.6 x 10^-19
Calculating the radius:
r = (1^2 x (6.626 x 10^-34)^2) / (4 x π^2 x 2.4 x 10^-26 x (1.6 x 10^-19)^2)
r = 0.02645 nm
Therefore, the radius of the first orbit of a He+ atom is 0.02645 nm, which corresponds to option D.
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