The correct answer is option 'C', G.W.F Hegel. G.W.F Hegel was a German philosopher who played a significant role in shaping the modern idea of the nation-state. His ideas about the state and its relationship with individuals and society had a profound influence on political philosophy and nationalism.

1. Hegel's Philosophy of the State:
Hegel viewed the state as the highest form of social organization, where the individual finds fulfillment and freedom. He believed that the state is an organic entity that represents the collective will and values of its citizens. According to Hegel, the state is not simply a political entity but also a moral and cultural institution that shapes the identity of its citizens.

2. Voluntary Participation:
Hegel argued that individuals willingly participate in the state and its institutions because they recognize it as a reflection of their own values and interests. This idea of voluntary participation forms the basis of modern nationalism, where individuals identify themselves with a particular nation and are willing to sacrifice for its well-being.

3. Unity and Diversity:
Hegel emphasized the importance of unity within the state while recognizing the existence of diverse cultural, linguistic, and regional identities. He believed that the state should provide a framework for maintaining harmony and resolving conflicts among different groups. This notion of unity in diversity has been influential in the formation of modern nation-states, which strive to accommodate diverse populations while fostering a sense of common identity.

4. Hegel's Influence on Nationalism:
Hegel's ideas about the state and nationalism influenced many prominent nationalist movements in the 19th and 20th centuries. Nationalists drew upon Hegel's concepts of the state as an organic entity and the importance of cultural and historical heritage to assert the rights and aspirations of their respective nations.

5. Legacy:
Hegel's philosophy of the state continues to shape political thought and has had a lasting impact on the development of nation-states worldwide. His ideas have provided a theoretical framework for understanding the relationship between the individual and the state, as well as the role of nationalism in shaping modern societies.

In conclusion, G.W.F Hegel's philosophy of the state, which emphasized the voluntary participation of individuals in a unified and diverse nation-state, has been instrumental in shaping the modern idea of the nation-state. His ideas have had a profound influence on political philosophy and nationalism, making him the key exponent of the modern idea of the nation-state.