Calculate The Energy Of The Violet Light Emitted By A Hydrogen Atom With A Wavelength Of 410.1 Nm.A. $4.85 \times 10^{-19} \, \text{J}$ B. $2.06 \times 10^{-19} \, \text{J}$ C. $1.23 \times 10^{-19} \, \text{J}$ D.
Introduction
In this article, we will explore the concept of calculating the energy of light emitted by a hydrogen atom. We will use the Rydberg formula to determine the energy of the violet light emitted by a hydrogen atom with a wavelength of 410.1 nm.
The Rydberg Formula
The Rydberg formula is a mathematical equation that describes the energy levels of a hydrogen atom. It is given by:
1/λ = R * (1/n1^2 - 1/n2^2)
where λ is the wavelength of the light emitted, R is the Rydberg constant, and n1 and n2 are the principal quantum numbers of the energy levels involved in the transition.
Calculating the Energy of the Violet Light
To calculate the energy of the violet light emitted by a hydrogen atom, we need to use the Rydberg formula. We are given the wavelength of the light emitted, which is 410.1 nm. We can use this value to calculate the energy of the light.
First, we need to convert the wavelength from nanometers to meters:
410.1 nm = 410.1 * 10^-9 m = 4.101 * 10^-7 m
Next, we can use the Rydberg formula to calculate the energy of the light. We know that the Rydberg constant is approximately 1.097 * 10^7 m^-1. We also know that the principal quantum numbers of the energy levels involved in the transition are n1 = 3 and n2 = 4.
Using the Rydberg formula, we can calculate the energy of the light as follows:
1/λ = R * (1/n1^2 - 1/n2^2) 1/(4.101 * 10^-7 m) = 1.097 * 10^7 m^-1 * (1/3^2 - 1/4^2) 1/(4.101 * 10^-7 m) = 1.097 * 10^7 m^-1 * (1/9 - 1/16) 1/(4.101 * 10^-7 m) = 1.097 * 10^7 m^-1 * (-0.0556 + 0.0625) 1/(4.101 * 10^-7 m) = 1.097 * 10^7 m^-1 * 0.0069 1/(4.101 * 10^-7 m) = 7.55 * 10^6 m^-1
Now, we can use the energy of the light to calculate the energy of the violet light emitted by the hydrogen atom. We can use the formula:
E = hc/λ
where E is the energy of the light, h is Planck's constant, c is the speed of light, and λ is the wavelength of the light.
Using the values of h = 6.626 * 10^-34 J s, c = 3 * 10^8 m/s, and λ = 4.101 * 10^-7 m, we can calculate the energy of the light as follows:
E = hc/λ E = (6.626 * 10^-34 J s) * (3 * 10^8 m/s) / (4.101 * 10^-7 m) E = 4.85 * 10^-19 J
Conclusion
In this article, we have calculated the energy of the violet light emitted by a hydrogen atom with a wavelength of 410.1 nm. We used the Rydberg formula to determine the energy of the light and then used the formula E = hc/λ to calculate the energy of the violet light emitted by the hydrogen atom. The calculated energy of the violet light is 4.85 * 10^-19 J.
Answer
Q: What is the Rydberg formula and how is it used to calculate the energy of light emitted by a hydrogen atom?
A: The Rydberg formula is a mathematical equation that describes the energy levels of a hydrogen atom. It is given by:
1/λ = R * (1/n1^2 - 1/n2^2)
where λ is the wavelength of the light emitted, R is the Rydberg constant, and n1 and n2 are the principal quantum numbers of the energy levels involved in the transition.
Q: What is the Rydberg constant and how is it used in the Rydberg formula?
A: The Rydberg constant is a fundamental constant of nature that describes the energy levels of a hydrogen atom. It is approximately equal to 1.097 * 10^7 m^-1.
Q: How is the energy of light calculated using the Rydberg formula?
A: To calculate the energy of light using the Rydberg formula, we need to know the wavelength of the light emitted and the principal quantum numbers of the energy levels involved in the transition. We can then use the formula:
E = hc/λ
where E is the energy of the light, h is Planck's constant, c is the speed of light, and λ is the wavelength of the light.
Q: What is the significance of the principal quantum numbers in the Rydberg formula?
A: The principal quantum numbers (n1 and n2) describe the energy levels of the hydrogen atom involved in the transition. The value of n1 and n2 determines the energy of the light emitted.
Q: Can the Rydberg formula be used to calculate the energy of light emitted by other atoms?
A: No, the Rydberg formula is specific to hydrogen atoms and cannot be used to calculate the energy of light emitted by other atoms.
Q: What is the relationship between the wavelength of light and its energy?
A: The wavelength of light is inversely proportional to its energy. This means that shorter wavelengths of light have higher energies, while longer wavelengths of light have lower energies.
Q: Can the energy of light be calculated using other methods besides the Rydberg formula?
A: Yes, the energy of light can be calculated using other methods, such as the Planck-Einstein equation and the Schrödinger equation.
Q: What is the significance of the energy of light in physics?
A: The energy of light is a fundamental concept in physics that describes the ability of light to do work. It is used to describe a wide range of phenomena, from the behavior of atoms and molecules to the properties of materials and the behavior of particles at the quantum level.
Q: Can the energy of light be measured experimentally?
A: Yes, the energy of light can be measured experimentally using a variety of techniques, including spectroscopy and interferometry.
Q: What are some common applications of the Rydberg formula in physics?
A: The Rydberg formula has a wide range of applications in physics, including:
- Calculating the energy of light emitted by hydrogen atoms
- Describing the behavior of atoms and molecules
- Understanding the properties of materials
- Studying the behavior of particles at the quantum level
Q: Can the Rydberg formula be used to calculate the energy of light emitted by other elements besides hydrogen?
A: No, the Rydberg formula is specific to hydrogen atoms and cannot be used to calculate the energy of light emitted by other elements.
Q: What is the relationship between the Rydberg formula and the Schrödinger equation?
A: The Rydberg formula is a simplified version of the Schrödinger equation, which is a more general equation that describes the behavior of particles at the quantum level.