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Answer:
Ionization potential of C⁺⁵ is 489.6 eV.
Wavelength of the transition from n=3 to n=2 is 1.83 x 10⁻⁸ m.
Explanation:
The ionization potential of hydrogen like atoms is given by the relation :
.....(1)
Here <em>E</em> is ionization potential, <em>Z</em> is atomic number and <em>n</em> is the principal quantum number which represents the state of the atom.
In this problem, the ionization potential of Carbon atom is to determine.
So, substitute 6 for <em>Z</em> and 1 for <em>n</em> in the equation (1).
<em> E = </em>489.6 eV
The wavelength (λ) of the photon due to the transition of electrons in Hydrogen like atom is given by the relation :
......(2)
R is Rydberg constant, n₁ and n₂ are the transition states of the atom.
Substitute 6 for Z, 2 for n₁, 3 for n₂ and 1.09 x 10⁷ m⁻¹ for R in equation (2).
= 5.45 x 10⁷
λ = 1.83 x 10⁻⁸ m
Given,
The initial inside diameter of the pipe, d₁=4.50 cm=0.045 m
The initial speed of the water, v₁=12.5 m/s
The diameter of the pipe at a later position, d₂=6.25 cm=0.065 m
From the continuity equation,
Where A₁ is the area of the cross-section at the initial position, A₂ is the area of the cross-section of the pipe at a later position, and v₂ is the flow rate of the water at the later position.
On substituting the known values,
Thus, the flow rate of the water at the later position is 5.99 m/s