The wavelength of the short radio waves, microwaves, ultraviolet waves are `lambda_(1),lambda_(2)` and `lambda_(3)`, respectively, Arrange them in decreasing order.

Options

A. `lambda_(1),lambda_(2),lambda_(3)`
B. `lambda_(1),lambda_(3),lambda_(2)`
C. `lambda_(3),lambda_(2),lambda_(1)`
D. `lambda_(2),lambda_(1),lambda_(3)`

Explanation

To solve the problem of arranging the wavelengths of short radio waves, microwaves, and ultraviolet waves in decreasing order, we can follow these steps:

### Step 1: Identify the Wavelength Ranges
- **Short Radio Waves (λ₁)**: The wavelength range is from \(1 \times 10^{-1}\) meters to \(1 \times 10^{4}\) meters.
- **Microwaves (λ₂)**: The wavelength range is from \(1 \times 10^{-3}\) meters to \(3 \times 10^{-1}\) meters.
- **Ultraviolet Waves (λ₃)**: The wavelength range is from \(1 \times 10^{-8}\) meters to \(4 \times 10^{-8}\) meters.

### Step 2: Compare the Wavelengths
To arrange the wavelengths in decreasing order, we need to compare the ranges:
- The maximum wavelength of short radio waves (λ₁) is \(1 \times 10^{4}\) meters, which is significantly larger than the maximum wavelength of microwaves (λ₂) at \(3 \times 10^{-1}\) meters.
- The maximum wavelength of microwaves (λ₂) is \(3 \times 10^{-1}\) meters, which is larger than the maximum wavelength of ultraviolet waves (λ₃) at \(4 \times 10^{-8}\) meters.

### Step 3: Establish the Order
From the comparisons:
- Since \(λ₁\) (short radio waves) has the largest range, followed by \(λ₂\) (microwaves), and finally \(λ₃\) (ultraviolet waves), we can conclude:
\[ λ₁ > λ₂ > λ₃ \]

### Step 4: Write the Final Answer
Thus, the arrangement of wavelengths in decreasing order is:
\[ λ₁, λ₂, λ₃ \]