Problem 12 - 43 Years JEE ADVANCED (1978-2020) + JEE MAIN Chapterwise & Topicwise Solved Papers Chemistry

Question

Which of the following statements is false? (a) Splitting of spectral lines in electrical field is called Stark effect (b) Frequency of emitted radiation from a black body goes from a lower wavelength to higher wavelength as the temperature increases (c) Photon has momentum as well as wavelength (d) Rydberg constant has unit of energy

Step-by-Step Solution

Answer

Statement (d) is false.

Step 1: Understand the Question

We are given four statements, and we need to determine which one is false. This involves confirming the accuracy of each statement individually.

Step 2: Analyze Statement (a)

This statement refers to the splitting of spectral lines in an electrical field known as the Stark effect. This is a true statement, as the Stark effect is indeed the splitting of atomic spectral lines due to an external electric field.

Step 3: Analyze Statement (b)

This statement suggests that as the temperature of a black body increases, the frequency of emitted radiation shifts from a lower wavelength to a higher wavelength. According to Wien's Displacement Law, as temperature increases, the peak wavelength of emission decreases, indicating higher frequency. Thus, this statement is true.

Step 4: Analyze Statement (c)

This statement asserts that photons have both momentum and wavelength. This is true per quantum mechanics principles, where a photon has momentum given by \( p = \frac{h}{\lambda} \), where \( h \) is Planck's constant and \( \lambda \) is the wavelength.

Step 5: Analyze Statement (d)

This statement claims that the Rydberg constant has the unit of energy. In reality, the Rydberg constant \( R \) is primarily used in calculations related to the wavelengths of photons and has units of inverse length (e.g., \( m^{-1} \) or \( cm^{-1} \)) rather than energy. Therefore, this statement is false.

Key Concepts

Stark Effect

The Stark Effect is a fascinating phenomenon in the world of quantum mechanics. It describes the splitting of atomic spectral lines when atoms are placed in an external electric field. This occurs because the external electric field perturbs the energy levels of the electrons within the atom. As a result, this causes a shift and splitting in the spectral lines, which are visible at the atomic level.

Here's what you need to understand about the Stark Effect:

• It is similar to the Zeeman effect, which involves splitting due to a magnetic field instead of an electric field.
• The Stark Effect can be observed in both emission and absorption lines.
• This effect is notably more complex in multi-electron atoms due to electron interactions.

The Stark Effect is significant as it has numerous applications, ranging from astrophysics to plasma physics, where it helps in diagnosing and understanding the behaviors of stars and gases.

Black Body Radiation

Black Body Radiation is an essential concept in understanding how objects emit radiation based on their temperature. A black body is an idealized object that absorbs all radiation falling upon it, without reflecting any, making it the perfect emitter when heated.

Some key points to remember about Black Body Radiation include:

• As a black body is heated, it emits radiation. The wavelength and intensity of this radiation depend on its temperature.
• Wien's Displacement Law tells us that the higher the temperature of the black body, the shorter the wavelength of its peak radiation emission.
• This means we observe a shift from lower wavelengths (longer) to higher wavelengths (shorter) with increased temperature.

Understanding Black Body Radiation is crucial for comprehending thermal emission processes, which have impactful applications in fields like thermal imaging and astrophysics.

Photon Momentum

In the realm of quantum mechanics, the concept of photons having momentum is both intriguing and fundamental. Photons, the quantum particles of light, do not have mass but they still possess momentum.

The principles of Photon Momentum are:

• Momentum for a photon is given by the equation \( p = \frac{h}{\lambda} \), where \( h \) is Planck's constant and \( \lambda \) is the wavelength of the photon.
• Even though photons lack mass, their momentum can exert pressure, known as radiation pressure.
• This feature of photons plays a role in technologies utilizing solar sails, where momentum from sunlight propels spacecraft.

Comprehending Photon Momentum is essential to grasp key phenomena such as light-matter interaction, which has various technological and scientific implications.

Rydberg Constant

The Rydberg Constant is a fundamental constant used in atomic physics, particularly in calculating the wavelengths of spectral lines in hydrogen and other elements. Its value is derived from the Rydberg formula, a classic equation in quantum mechanics.

Understanding the Rydberg Constant includes:

• It is primarily used to determine the energy differences between electron orbitals.
• The constant has units of inverse length, such as \( m^{-1} \), and not energy, which differentiates it from quantities like ionization energy.
• The Rydberg formula helps predict the wavelengths of photons emitted during electron transitions in an atom.

The Rydberg Constant not only helps explain spectral lines in hydrogen but also serves as a benchmark in precision measurements in spectroscopy and quantum calculations.