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On the basis of Bohr's model, the radius of the 3rd orbit is -
- a)Equal to the radius of first orbit
- b)Three times the radius of first orbit
- c)Five times the radius of first orbit
- d)Nine time the radius of first orbit
Correct answer is option 'D'. Can you explain this answer?
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The correct answer is option 'D', which states that the radius of the 3rd orbit in Bohr's model is nine times the radius of the first orbit. Let's understand this in detail:
Bohr's Model of the Atom:
- Bohr's model was proposed by Danish physicist Niels Bohr in 1913 to explain the behavior of electrons in an atom.
- According to this model, electrons revolve around the nucleus in well-defined orbits or energy levels.
- Each orbit or energy level is characterized by a specific energy value. The energy of the electron is quantized, meaning it can only have certain discrete values.
Explanation:
- In Bohr's model, the radius of each orbit is related to its energy level. The higher the energy level, the larger the radius of the orbit.
- The formula to calculate the radius of an electron orbit in Bohr's model is given by:
r = (0.529 Å) * n^2 / Z
where r is the radius of the orbit, n is the principal quantum number (energy level), and Z is the atomic number of the atom.
Note: 0.529 Å is the Bohr radius, which is a constant value.
- We are given that the radius of the 3rd orbit is nine times the radius of the first orbit. Let's denote the radius of the first orbit as r1 and the radius of the third orbit as r3.
- According to the given information, we have:
r3 = 9 * r1
- Now, let's substitute the values in the formula for r1 and r3:
(0.529 Å) * 1^2 / Z = r1
(0.529 Å) * 3^2 / Z = r3
- Dividing the equation for r3 by the equation for r1, we get:
r3 / r1 = ((0.529 Å) * 3^2 / Z) / ((0.529 Å) * 1^2 / Z)
r3 / r1 = (0.529 Å * 9 / Z) / (0.529 Å / Z)
r3 / r1 = 9
- Therefore, we have shown that the radius of the 3rd orbit is nine times the radius of the first orbit in Bohr's model.
- Hence, the correct answer is option 'D' - Nine times the radius of the first orbit.
Bohr's Model of the Atom:
- Bohr's model was proposed by Danish physicist Niels Bohr in 1913 to explain the behavior of electrons in an atom.
- According to this model, electrons revolve around the nucleus in well-defined orbits or energy levels.
- Each orbit or energy level is characterized by a specific energy value. The energy of the electron is quantized, meaning it can only have certain discrete values.
Explanation:
- In Bohr's model, the radius of each orbit is related to its energy level. The higher the energy level, the larger the radius of the orbit.
- The formula to calculate the radius of an electron orbit in Bohr's model is given by:
r = (0.529 Å) * n^2 / Z
where r is the radius of the orbit, n is the principal quantum number (energy level), and Z is the atomic number of the atom.
Note: 0.529 Å is the Bohr radius, which is a constant value.
- We are given that the radius of the 3rd orbit is nine times the radius of the first orbit. Let's denote the radius of the first orbit as r1 and the radius of the third orbit as r3.
- According to the given information, we have:
r3 = 9 * r1
- Now, let's substitute the values in the formula for r1 and r3:
(0.529 Å) * 1^2 / Z = r1
(0.529 Å) * 3^2 / Z = r3
- Dividing the equation for r3 by the equation for r1, we get:
r3 / r1 = ((0.529 Å) * 3^2 / Z) / ((0.529 Å) * 1^2 / Z)
r3 / r1 = (0.529 Å * 9 / Z) / (0.529 Å / Z)
r3 / r1 = 9
- Therefore, we have shown that the radius of the 3rd orbit is nine times the radius of the first orbit in Bohr's model.
- Hence, the correct answer is option 'D' - Nine times the radius of the first orbit.
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On the basis of Bohr's model, the radius of the 3rd orbit is -a)Equal to the radius of first orbitb)Three times the radius of first orbitc)Five times the radius of first orbitd)Nine time the radius of first orbitCorrect answer is option 'D'. Can you explain this answer?
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