What is the resistance ofa wire made of a material with resistivity of 3.2 x 10^-8 Ω.m if its length is 2.5 m and its diameter i
1 answer:
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Answer:
a. 30 N / m
b. 9.0 N
Explanation:
Given that
Unstretched length of the spring, = 20.0cm = 0.2m
a) When the mass of 4.5N is hanging from the second spring, then extended length Is
= 35.0cm = 0.35m
So, the change in spring length when mass hangs is
= (0.35 - 0.20) m
= 0.15m
As spring are identical
Let us assume that the spring constant be "k", so at equilibrium
Restoring Force on spring = Block weightage
kx = W = 4.50
= 30 N / m
b) Now for the third spring, stretched the length of spring is
= 50cm = 0.5m
So, the change in spring length is
= (0.5-0.20)m
= 0.30m
At equilibrium,
Restoring Force on spring = Block weightage
Now using all mentioned and computed values in above,
= 30(0.3)
= 9.0 N
Answer:
The correct option that represents an acceptable set of quantum numbers for an electron in an atom is;
(b) 4, 3, -3, 1/2.
Explanation:
To solve the question, we note that the available options where the set of quantum numbers for an electron in an atom are arranged as n, l, m l , and ms are;
4, 4, 4, 1/2
4, 3, -3, 1/2
4, 3, 0, 0
4, 5, 7, -1/2
4, 4, -5, 1/2
Let us label them as a to as follows
(a) 4, 4, 4, 1/2
(b) 4, 3, -3, 1/2
(c) 4, 3, 0, 0
(d) 4, 5, 7, -1/2
(e) 4, 4, -5, 1/2
Next we note the rules for the assignment and arrangement of quantum numbers are as follows
Number Symbol Possible values
Principal Quantum Number .......n........................1, 2, 3, ......n
Angular momentum quantum
number...............................................l.........................0, 1, 2, .......(n - 1)
Magnetic Quantum Number........m₁......................-l, ..., -1, 0, 1,.....,l
Spin Quantum Number.................m.....................+1/2, -1/2
We are meant to analyze each of the arrangement for acceptability.
Therefore for (a),
we note that the angular momentum quantum number, l =4 , is equal to the principal quantum number n =4 which violates the rule as the maximum value of the angular momentum quantum number is (n-1) where the maximum value of the principal quantum number is n.
Therefore (a) is not acceptable.
(b) Here we note that
The principal quantum number n = 4 ∈ (1, 2, 3, ......n) → acceptable
The angular momentum quantum number l = 3 ∈ (0, 1, 2, .......(n - 1)) → acceptable
The magnetic quantum number m₁ = -3 ∈ (-l, ..., -1, 0, 1,.....,l) → acceptable
The spin quantum number m = 1/2 ∈ (+1/2, -1/2) → acceptable
Therefore (b) 4, 3, -3, 1/2 represents an acceptable set of quantum numbers for an electron in an atom.
(c) Here we have
The principal quantum number n = 4 ∈ (1, 2, 3, ......n) → acceptable
The angular momentum quantum number l = 3 ∈ (0, 1, 2, .......(n - 1)) → acceptable
The magnetic quantum number m₁ = 0 ∈ (-l, ..., -1, 0, 1,.....,l) → acceptable
The spin quantum number m = 0 ∉ (+1/2, -1/2) → not acceptable
Therefore (c) 4, 3, 0, 0 does not represents an acceptable set of quantum numbers for an electron in an atom.
(d) Here we have;
The principal quantum number n = 4 ∈ (1, 2, 3, ......n) → acceptable
The angular momentum quantum number l = 5 ∉ (0, 1, 2, .......(n - 1)) → not acceptable
The magnetic quantum number m₁ = 7 ∉ (-l, ..., -1, 0, 1,.....,l) → acceptable
The spin quantum number m = -1/2 ∈ (+1/2, -1/2) → acceptable
Therefore (d) 4, 5, 7, -1/2 does not represents an acceptable set of quantum numbers for an electron in an atom.
(e) Here we have;
The principal quantum number n = 4 ∈ (1, 2, 3, ......n) → acceptable
The angular momentum quantum number l = 4 ∉ (0, 1, 2, .......(n - 1)) → not acceptable
The magnetic quantum number m₁ = -5 ∉ (-l, ..., -1, 0, 1,.....,l) → acceptable
The spin quantum number m = 1/2 ∈ (+1/2, -1/2) → acceptable
Therefore (e) 4, 4, -5, 1/2 does not represents an acceptable set of quantum numbers for an electron in an atom.