The Solution Of $r ^ { 2 } R ^ { \prime \prime } + r R ^ { \prime } + \lambda R = 0 , R ( 0 ) = 0 , R ( 1 ) = 0$

question 24

Multiple Choice

The solution of $r ^ { 2 } R ^ { \prime \prime } + r R ^ { \prime } + \lambda R = 0 , R ( 0 ) = 0 , R ( 1 ) = 0$ is

• A) \(\lambda = n \pi , R = \sin ( n \pi \ln r )\)
• B) \(\lambda = ( n \pi ) ^ { 2 } , R = \sin ( n \pi \ln r )\)
• C) \(\lambda = ( n \pi ) ^ { 2 } , R = \sin ( n \pi \ln r ) + \cos ( n \pi \ln r )\)
• D) \(\lambda = n \pi , R = \sin ( n \pi \ln r ) - \cos ( n \pi \ln r )\)
• E) none of the above

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Definitions:

Neutrons

Subatomic particles found within an atom's nucleus, possessing no electric charge and contributing to the atom's mass.

Protons

Protons are subatomic particles found in the nucleus of an atom with a positive electric charge.

Electrons

Subatomic particles with a negative charge, found in all atoms and playing a key role in chemical reactions and electricity.

Hydrogen Bonding

A weak type of chemical bond that is common in water and organic compounds, forming between a hydrogen atom and a more electronegative atom.