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In which of the following systems will the radiusof the first orbit (n = 1) be minimum ? [2003]
- a)Hydrogen atom
- b)Doubly ionized lithium
- c)Singly ionized helium
- d)Deuterium atom
Correct answer is option 'B'. Can you explain this answer?
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In which of the following systems will the radiusof the first orbit (n...
Z(=3) is maximum for Li2+.Most Upvoted Answer
In which of the following systems will the radiusof the first orbit (n...
Answer:
The radius of the first orbit (n = 1) in an atom is determined by the Bohr's formula:
r = 0.529 Å * n^2 / Z
where r is the radius of the orbit, n is the principal quantum number, and Z is the atomic number of the atom.
Let's analyze the given options one by one:
a) Hydrogen atom:
The atomic number of hydrogen is 1, so Z = 1. For the first orbit (n = 1), the radius of the hydrogen atom is:
r = 0.529 Å * 1^2 / 1 = 0.529 Å
b) Doubly ionized lithium:
The atomic number of lithium is 3. Since it is doubly ionized, it has lost two electrons, leaving only one electron in the system. Therefore, Z = 1 for the remaining electron. For the first orbit (n = 1), the radius of the doubly ionized lithium atom is:
r = 0.529 Å * 1^2 / 1 = 0.529 Å
c) Singly ionized helium:
The atomic number of helium is 2. Since it is singly ionized, it has lost one electron, leaving only one electron in the system. Therefore, Z = 1 for the remaining electron. For the first orbit (n = 1), the radius of the singly ionized helium atom is:
r = 0.529 Å * 1^2 / 1 = 0.529 Å
d) Deuterium atom:
Deuterium is an isotope of hydrogen with an atomic number of 1. For the first orbit (n = 1), the radius of the deuterium atom is:
r = 0.529 Å * 1^2 / 1 = 0.529 Å
From the above analysis, we can see that the radius of the first orbit (n = 1) is the same for all the given options, which is 0.529 Å. Therefore, the correct answer is option 'B' - Doubly ionized lithium.
The radius of the first orbit (n = 1) in an atom is determined by the Bohr's formula:
r = 0.529 Å * n^2 / Z
where r is the radius of the orbit, n is the principal quantum number, and Z is the atomic number of the atom.
Let's analyze the given options one by one:
a) Hydrogen atom:
The atomic number of hydrogen is 1, so Z = 1. For the first orbit (n = 1), the radius of the hydrogen atom is:
r = 0.529 Å * 1^2 / 1 = 0.529 Å
b) Doubly ionized lithium:
The atomic number of lithium is 3. Since it is doubly ionized, it has lost two electrons, leaving only one electron in the system. Therefore, Z = 1 for the remaining electron. For the first orbit (n = 1), the radius of the doubly ionized lithium atom is:
r = 0.529 Å * 1^2 / 1 = 0.529 Å
c) Singly ionized helium:
The atomic number of helium is 2. Since it is singly ionized, it has lost one electron, leaving only one electron in the system. Therefore, Z = 1 for the remaining electron. For the first orbit (n = 1), the radius of the singly ionized helium atom is:
r = 0.529 Å * 1^2 / 1 = 0.529 Å
d) Deuterium atom:
Deuterium is an isotope of hydrogen with an atomic number of 1. For the first orbit (n = 1), the radius of the deuterium atom is:
r = 0.529 Å * 1^2 / 1 = 0.529 Å
From the above analysis, we can see that the radius of the first orbit (n = 1) is the same for all the given options, which is 0.529 Å. Therefore, the correct answer is option 'B' - Doubly ionized lithium.
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