An upper limit is set on the amount of energy that can be absorbed or emitted in oscillations. | |

A lower limit is set on the amount of energy that can be absorbed or emitted in oscillations. | |

The energy of the oscillations of atoms within molecules can have any value. | |

The energy of the oscillations of atoms
within molecules must be quantized. |

## Answer

## General guidance

The concept used to solve the problem is Planck’s quantum hypothesis. Initially, the Planck’s quantum hypothesis is expressed as a function of frequency and Planck’s constant. Later, the energy of the atoms is considered, and energy of the oscillation is expressed. Finally, the correct statement is chosen from the concept of Quantum Hypothesis.

According to quantum Hypothesis, the energy can be emitted or absorbed only in quanta. Quanta are the discrete energy bundles.
According to Planck’s quantum Hypothesis, the energy of the atoms is expressed as:
Here, *f *is the frequency of light and *h* is Planck’s constant.
The energy of the atoms within the molecules is quantized as is expressed as whole number multiple quanta. The expression for the energy of the atoms is expressed as:
Here, *n* is the number of quanta particles, *f *is the frequency of light and *h* is Planck’s constant.
The atoms in the molecules are often stable. The atoms due to its lower energy are bound as molecules. If the atoms in the molecules absorb energy, the atoms are excited to the higher energy level.
Similarly, the atoms at a higher energy level will emit energy. Atoms are emitting energy come down to the lower energy and thereby becoming stable.

## Step-by-step

### Step 1 of 2

The energy of the oscillations of atoms is expressed as:
The energy here is an integral multiple of . The energy emitted or absorbed is in multiples of quanta.
The energy present is expressed as a function of which is quantized. The energy of the oscillations is within the molecule with any value is incorrect.
The upper value of energy cannot be determined as the energy depends on *n *or quanta value. The energy is directly proportional to the quanta number.
The relation between energy and quanta is expressed as:

**The incorrect statement is an upper limit is set on the amount of energy that can be absorbed or emitted in oscillations and energy of the oscillations of atoms within the molecules can have any value. **

The energy of the oscillation is a quantized and hence emits or absorbs energy in integral multiples of *hf*.

### Step 2 of 2

The lowest energy that can be emitted or absorbed is calculated as:
Substitute 1 for *n,* and find the lowest energy possible.
The lowest energy possible is .
The lowest energy can only be determined. The upper limit cannot be determined.
The quantized energy level is expressed as:

Hence, the energy of the oscillations of the atoms within the molecules is quantized.

**The correct statements are – a lower limit is set on the amount of energy that can be absorbed or emitted in oscillations and energy of the oscillations of atoms within molecules must be quantized.**

The lower energy limit depends on the *n* value or the quanta number and the frequency of the atom on emission.

### Answer

**The incorrect statement is an upper limit is set on the amount of energy that can be absorbed or emitted in oscillations and energy of the oscillations of atoms within the molecules can have any value. **

**The correct statements are – a lower limit is set on the amount of energy that can be absorbed or emitted in oscillations and energy of the oscillations of atoms within molecules must be quantized.**

### Answer only

**The incorrect statement is an upper limit is set on the amount of energy that can be absorbed or emitted in oscillations and energy of the oscillations of atoms within the molecules can have any value. **

**The correct statements are – a lower limit is set on the amount of energy that can be absorbed or emitted in oscillations and energy of the oscillations of atoms within molecules must be quantized.**