Out of `Be, Mg, Ca, Sr`and `Ba` total number of metals whose nitrates are decomposed according to following reaction.
`2M(NO_(3))_(2) overset(/_\)(to) 2MO+4NO_(2)+O_(2)`

Explanation

To solve the question regarding the decomposition of nitrates of the metals Beryllium (Be), Magnesium (Mg), Calcium (Ca), Strontium (Sr), and Barium (Ba), we will analyze the decomposition reaction for each metal's nitrate.

### Step-by-Step Solution:

1. **Identify the Reaction**: The given decomposition reaction is:
\[ 2M(NO_3)_2 \xrightarrow{\Delta} 2MO + 4NO_2 + O_2 \]
This indicates that when the nitrate of a metal (M) is heated, it decomposes to form metal oxide (MO), nitrogen dioxide (NO2), and oxygen (O2).

2. **Analyze Each Metal's Nitrate**:
- **Beryllium Nitrate (Be(NO3)2)**:
\[ 2Be(NO_3)_2 \xrightarrow{\Delta} 2BeO + 4NO_2 + O_2 \]
This reaction occurs upon heating.

- **Magnesium Nitrate (Mg(NO3)2)**:
\[ 2Mg(NO_3)_2 \xrightarrow{\Delta} 2MgO + 4NO_2 + O_2 \]
This reaction also occurs upon heating.

- **Calcium Nitrate (Ca(NO3)2)**:
\[ 2Ca(NO_3)_2 \xrightarrow{\Delta} 2CaO + 4NO_2 + O_2 \]
This reaction occurs upon heating as well.

- **Strontium Nitrate (Sr(NO3)2)**:
\[ 2Sr(NO_3)_2 \xrightarrow{\Delta} 2SrO + 4NO_2 + O_2 \]
This reaction occurs upon heating.

- **Barium Nitrate (Ba(NO3)2)**:
\[ 2Ba(NO_3)_2 \xrightarrow{\Delta} 2BaO + 4NO_2 + O_2 \]
This reaction also occurs upon heating.

3. **Conclusion**: All five metals (Be, Mg, Ca, Sr, Ba) have nitrates that decompose according to the given reaction when heated. Therefore, the total number of metals whose nitrates decompose in this manner is **5**.

### Final Answer:
The total number of metals whose nitrates decompose according to the reaction is **5**.