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What is the energy (in joules) and the wavelength (in meters) of the line in the spectrum of hydrogen that represents the movement of an electron from bohr orbit with n = 2 to the orbit with n = 5? in what part of the electromagnetic spectrum do we find this radiation?

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Answer from: hbked23

The energy is $4.57x10^{-19} J$ and the wavelength is $4.34x10^{-7}m$ for the line in the spectrum of hydrogen that represents the movement of an electron from Bohr orbit with n = 2 to the orbit with n = 5.

In what part of the electromagnetic spectrum do we find this radiation?

In the Ultraviolet part of the electromagnetic spectrum.

Explanation:

The energy of the absorbed photon can be known by the difference in energy between the two states in which the transition is happening (In this case from n = 2 to n = 5):

$E = E_{upper}-E_{lower}$ (1)

The permitted energy for the atom of hydrogen, according with the Bohr's model, is defined as:

$E_{n} = -\frac{13.606 eV}{n^{2}}$ (2)

Or it can be expressed in Joules, since $1eV = 1.60x10^{-19}J$

$E_{n} = -\frac{2.18x10^{-18} J}{n^{2}}$ (3)

Where the value $-2.18x10^{-18}$ represents the energy of the ground state¹ and n is the principal quantum number.

For the case of n = 2:

$E_{2} = -\frac{2.18x10^{-18} J}{(2)^{2}}$

$E_{2} = -5.45x10^{-19} J$

For the case of n = 5:

$E_{5} = -\frac{2.18x10^{-18} J}{(5)^{2}}$

$E_{5} = -8.72x10^{-20} J$

Replacing those values in equation (1) it is gotten:

$E = -8.72x10^{-20} J-(-5.45x10^{-19} J )$

$E = 4.57x10^{-19} J$

The wavelength can be determined by means of the Rydberg formula:

$\frac{1}{\lambda} = R(\frac{1}{n_{l}^{2}}-\frac{1}{n_{u}^{2}})$ (4)

Where R is the Rydberg constant, with a value of $1.097x10^{7}m^{-1}$

For this particular case $n_{l} = 2$ and $n_{u} = 5$ :

$\frac{1}{\lambda} = 1.097x10^{7}m^{-1}(\frac{1}{(2)^{2}}-\frac{1}{(5)^{2}})$

$\frac{1}{\lambda} = 1.097x10^{7}m^{-1}(0.21)$

$\frac{1}{\lambda} = 2303700m^{-1}$

$\lambda = \frac{1}{2303700m^{-1}}$

$\lambda = 4.34x10^{-7}m$

So the energy is $4.57x10^{-19} J$ and the wavelength is $4.34x10^{-7}m$ for the line in the spectrum of hydrogen that represents the movement of an electron from Bohr orbit with n = 2 to the orbit with n = 5.

In what part of the electromagnetic spectrum do we find this radiation?

In the Ultraviolet part of the electromagnetic spectrum.

Key terms:

¹Ground state: State of minimum energy.

Answer from: Quest

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Answer from: Quest

answer

procedural programming, object-oriented programming

explanation

procedural programming is a type of computer programming language that specifies a series of well structured steps and procedures within its development period of time. it contains a systematic order of statements, functions and commands to complete a computational task or program. it is centered on creating procedures. while object oriented programming is a programming language that is centered on creating objects rather that actions and data rather than logic.. it has four principles which are inheritance, polymorphism, abstraction and encapsulation